Show and explain all of the steps used in order to simplify the following rational expression 3x^(2)-3x / 3x^(3)-6x^(2)+3x to 1 / x-1.

Answers

Answer 1

Answer:

3x^2 + x^4 - x^3 + 3 - 6x

Step-by-step explanation:

Find Least Common Multiplier of 3x^(2)-3x / 3x^(3)-6x^(2)+3x to 1 / x-1

3x^2 - 3 . x/3 x^3 - 6x^2 + 3x

Apply exponent rule: a^b + c = a^b a^c

x^2 = xx, x^3 x/3 = xx^2, x^2 = xx

= 3xx - 3xxx - 6xx + 3x

Rewrite -6 as 2 . 3

= 3xx - 3xxx + 2 . 3xx + 3x

Factor out common term 3x

= 3x(x - x^2(x/3) -2x + 1)

= 3x(- x^3/3 - x + 1)

Multiply each factor with the highest power:

(- x^3/3 - x + 1) . 3 . (1/x - 1\) . x

Simplify

3x^2 + x^4 - x^3 + 3 - 6x


Related Questions

Which of the following is not a property of quadrilaterals?

A.
There are four sides.
B.
There are four diagonals.
C.
There are four vertices.
D.
The measures of the interior angles add up to 360 degrees


Please select the best answer from the choices provided

Answers

Answer:

The correct answer for this question is letter "(B) There are four diagonals." It is not a property of quadrilaterals.

Answer:

b

it has 2 diagonals crossing each other

Rate of Change: Based on the equation determine the rate of change by looking at the coefficients.

Hint: Remember: y=mx+b (m=slope)

1. y=-x+ 3
2. y=3x-1
3. y= 8 + x2

Answers

Answer:

1) -1

2) 3

3) 2

Explain the land resource of Nepal according to ecological division. (NOT EXPECTING ANY SILLY ANSWERS)​

Answers

Answer:

nepal is a land locked country.it is surrounded by india from eas west and south and chime form north

according to ecological fivison it is divided into three region

1.terai

2.hilly

3. himalyan

In hilly region there is more production of crops and vegetables . peplo come in terai region to sell vegetables and they do work with unity .

thry have their own work.so they work in unity which help to terai region grow crops and hilly region sell it in Himalayan region from which terai help to grow crops usually there is a fertile land and it occupies 42%.

Determine the axis of symmetry and the vertex of the given function.

Answers

The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y=ax2+bx+c , the axis of symmetry is a vertical line x=−b2a .

Solve for t. 4=1/2gt^2

Answers

Answer:

[tex]4=1/2gt^{2}[/tex]

Multiply equation by 2/g

4(2/g) = t²

t = √(8/g)

t = 2√(2/g)

[tex]answer:t=\sqrt{\frac{8}{g} }[/tex]

OAmalOHopeO

A man earned $3000 the first year he worked. If he received a raise of $600 at the end of each year, what was his salary during the 15th year?

A) $8400
B) None of these
C) $11,400
D) $12,000

Answers

Answer:

$11,400

Step-by-step explanation:

3,000+14(600)=11,400

We know that it expands by $600 a year and we are looking for the salary during the 15th year.  During the 15th year, it could be using the salary of the 14th year since it is during not after.  We then add that to the base salary of $3,000 so then we have $11,400.

In Exercises 51−56, the letters a, b, and c represent nonzero constants. Solve the equation for x
bx = -7

Answers

Answer:

x = -7/b

Step-by-step explanation:

bx = -7

Divide each side by b

bx/b = -7/b

x =-7/b

Given :

Solve the equation for x : bx = -7

Solution :

Here we are provided to find for x so from the equation by cross multiplying we will remove b to the right hand side of the equation and then we can get x

bx = -7

Now, to cross multiply

x = -7/b

Therefore, the required answer is -7/b

In 60 words or fewer, write what you think the term economy means. Think about how money fits into your definition.

Answers

Step-by-step explanation:

An economy is made up of every single activity that has to do with production, consumption, and the buying and selling of goods or rendering services.

In an economy there are combinations of market transactions and decisions made collectively or in hierarchy. Individuals, families, businesses, governments make up the decision-making process.

Money is the legal tender of an economy. It is the medium of exchange that an economy uses for transactions.

Instructions: Find the measure of the indicated angle to the nearest
degree
21
?
40
?=

Answers

Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.

Remember: SOH-CAH-TOA

Looking from the angle, we know the opposite side and the hypotenuse. Therefore, we should use the sine function.

sin(x) = 21/40

x = sin^-1(21/40)

x = 32 degrees

Hope this helps!

Pls help me in this question

Answers

Answer:

3

Step-by-step explanation:

since the diagonal are equal in length

6x-8=2x+4

4x=12

x=3

What is the area of Figure ABCD? PLS HELP 50 POINTS PLSSSSSSSSSSSSSSSSSSSS
BEST ANSWER GET BRAINLY

Answers

Answer:

112 in^2

Step-by-step explanation:

First find the area of the rectangle

A = l*w = 14*7 =98

Then find the area of the triangle

A = 1/2 bh = 1/2 (18-14) *7 = 1/2 (4)*7 = 14

Add the areas together

98+14 =112

Hello!

[tex]\large\boxed{A = 112in^2}[/tex]

We can use the formula for the area of a trapezoid to solve:

A = 1/2(b1 + b2) · h

Thus:

A = 1/2(18 + 14) · 7

Simplify:

A = 1/2(32) · 7

A = 16 · 7

A = 112 in²

ASAPPPPPPPPPPPPPPPPPPPPPPPPPP HELPPPPPPPPPPPPPPPPPPPPP PLEASEEEEEE

Answers

Answer:

- 3 / 10

Step-by-step explanation:

- 9 / 10 - ( - 3 / 5 )

= - 9 / 10 + 3 / 5

= 3 / 5 - 9 / 10

= 6 / 10 - 9 / 10

= ( 6 - 9 ) / 10

= - 3 / 10

Using the given image and congruency markings ,type in the triangle that is congruent with the given triangle below.

Answers

Answer:

GHI is congruent to HGW

Step-by-step explanation:

PLEASE HELP!! what is the value of x?

Answers

Answer:

[tex]\frac{3x}{4x} =\frac{3x+7}{5x-8}[/tex]

[tex]\frac{3}{4} =\frac{3x+7}{5x-8}\: (cross\: multiply)[/tex]

[tex]3(5x-8)=4(3x+7)[/tex]

[tex]15x-24=12x+28\\+24~~~~~~~~~~~~+24[/tex]

[tex]15x=12x+52\\-12x~~~~-12x\\-------\\3x=52[/tex]

[tex]\frac{3x}{3} =\frac{52}{3}[/tex]

[tex]x=52/3[/tex]

[tex]Answer:C[/tex]

-------------------------

Hope it helps...

Have a great day!!

Solve the inequality.
X-5 < 16
A. X> 21
B. x<21
C. x< 11
D. x> 11

Answers

Answer:

x < 21

Step-by-step explanation:

x - 5 < 16

x < 21           Add 5 to both sides

Answer:

B. x < 21

Step-by-step explanation:

x - 5 < 16

  +5    +5

x      <  21

The answer would be B.

A) If {3,1,-1,-3} is the range of the function f(x) =2x+3/5, find its domain.
B) Which element in the range has pre-image 8 under the function of f:x->3x+1/5? ​

Answers

Answer:

64

Step-by-step explanation:

1=879=96889=

The demand function for Widgets is given by the equation P = 14 – 0.39Q, and the supply function is
given by the equation P = 0.61Q + 12. Find the market equilibrium price for Widgets.

Answers

Answer:

Equilibrium price for widgets = 13.22

Step-by-step explanation:

At equilibrium, quantity demand, Qd = quantity supplied, Qs

Demand

P = 14 – 0.39Q

P - 14 = - 0.39Q

Q = (P - 14) / - 0.39

Supply

P = 0.61Q + 12

P - 12 = 0.61Q

Q = (P - 12) / 0.61

Qd = Qs

(P - 14) / - 0.39 = (P - 12) / 0.61

Cross product

(P - 14) * 0.61 = - 0.39 * (P - 12)

0.61P - 8.54 = - 0.39P + 4.68

0.61P + 0.39P = 4.68 + 8.54

P = 13.22

Check

Q = (P - 14) / - 0.39

= (13.22 - 14) / - 0.39

= -0.78 / -0.39

= 2

Q = (P - 12) / 0.61

= (13.22 - 12) / 0.61

= 1.22 / 0.61

= 2

Therefore,

Equilibrium price for widgets = 13.22

Equilibrium quantity = 2

The cost price of an electric fan is Rs. 2800. If the shopkeeper marks its price 30℅ above the cost price and sells it at 10℅ discount, how much should a customer pay for it with 15℅ VAT?

Answers

Answer:

The customer will pay along with VAT = Rs 3767.4

Step-by-step explanation:

Cost price of an electric fan = 2800

Pirce after 30% above the cost price = 2800 + (30% of 2800 = 3640

Selling price after 10% discount = 3640 - (10% of 3640) = 3276

Now 15% VAT = 3276 x 15%

15% VAT = 491.4

The customer will pay along with VAT = 3276 + 491.4  

The customer will pay along with VAT = Rs 3767.4

what is the value of i^n if the remained of n/4 is 2
A. i
B. -i
C. -1
D. 1

Answers

Answer:

5

Step-by-step explanation:

Make d the subject h=d/3+2

Answers

Answer:

[tex]d = 3h - 6[/tex]

Step-by-step explanation:

Step 1:  Solve for d

I am assuming that you are asking for me to solve for the variable d.  Let me know if what I am doing is not what you want.

[tex]h = \frac{d}{3} + 2[/tex]

[tex]h - 2 = \frac{d}{3} + 2 - 2[/tex]

[tex](h - 2) * 3 = \frac{d}{3} * 3[/tex]

[tex]3h - 6 = d[/tex]

Answer:  [tex]d = 3h - 6[/tex]

please help me (geometry)

Answers

Answer:

True

Step-by-step explanation:

When two lines are parallel, the corresponding angles formed by the transversal (intersecting line) are congruent. This is called the corresponding angles postulate. It can be used in reverse: if two corresponding angles are congruent, then the non-transversal lines are parallel.

Answer:

Step-by-step explanation:

Angles 4 and 5 are corresponding; this means that they are sitting in the same places within their angle "bunch" for lack of a better word. We are then told that they are are congruent which means that they have the exact same measure. Corresponding angles can exist without being congruent, but because they are, that means that A and B HAVE to be parallel. So true.

Rose’s checking account has a balance of Negative 54 dollars. She makes no more withdrawals but deposits $15 per day in her account over the next five days. On the sixth day, she makes no deposits, but the bank charges a maintenance fee of $5. What is the balance in her account on the sixth day? $16 $26 $124 $134

Answers

Answer:

16

Step-by-step explanation:

Her account balance on the sixth day is sixteen. This is because -54 +75 is 21 then you subtract 5 and get 16. (15 times 5 is 75)  

Answer:

16

Step-by-step explanation:

Starting balance: -54

Deposits +15

                +15

                 +15

                 +15

                +15

for a  total of +75

-54+75 = 21

Maintenance fee: - 5

21 - 5 = 16

Use elimination to solve the system 4x + 7y = –14 and 8x + 5y = 8 for x. Round to the nearest tenth.

Answers

Answer:

X= 7/2

Step-by-step explanation:

Multiply first equation by -2 and second equation by 1

-2(4x+7y=-14)

1(8x+5y= 8)

= -8x -14y =28

8x+5y=8

Add these equations to eliminate X:

-9y=36

-9y/-9 = 36/-9

y=- 4

Plug in Y to find X

4x + 7y = -14

4x+7(-4) = -14

4x-28+28= -14+28

4x= 14

X= 7/2

Answered by Gauthmath

Answer: x=3 and 1/2

Step-by-step explanation: Happy to Help (0.<)

Determine which quadratic equation has two
non-real solutions.

Answers

Answer:

Hello,

answer C : -3x²-3x-2=0 (or 3x²+3x+2=0)

Step-by-step explanation:

A: delta=12²-4*2*18=0 not negative

B: delta= 5²+4*3*1=37 not negative

C: 3x²+2x+2=0, delta=2²-4*3*2=16-24=-8 is negative: roots are complex

D: delta 16²-4*2*2=240 not negative

combine like terms and simplify (−3 + 4x2 − 4x) + (−1 − 3x2− 4)

Answers

Answer:

x² - 4x - 8

General Formulas and Concepts:

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify

(-3 + 4x² - 4x) + (-1 - 3x² - 4)

Step 2: Simplify

Combine like terms (x²):                                                                                   x² - 3 - 4x - 1 - 4Combine like terms:                                                                                         x² - 4x - 8

What is the product? StartFraction 3 k Over k + 1 EndFraction times StartFraction k squared minus 1 Over 3 k cubed EndFraction StartFraction k + 1 Over k squared EndFraction StartFraction k minus 1 Over k squared EndFraction StartFraction negative 1 Over k EndFraction StartFraction 1 Over k EndFraction

Answers

Answer:

StartFraction negative 1 Over k cubed EndFraction

Step-by-step explanation:

3k / (k + 1) × (k²- 1) / 3k³

= 3k(k² - 1) / (k + 1)(3k³)

= 3k³ - 3k / 3k⁴ + 3k³

= -3k / 3k⁴

= -1/k³

StartFraction k + 1 Over k squared EndFraction

(k + 1) / k²

StartFraction k minus 1 Over k squared EndFraction

(k - 1)/k²

StartFraction negative 1 Over k cubed EndFraction

= -1/k³

StartFraction 1 Over k EndFraction

= 1/k

Answer:

B: k - 1 / k^2

Step-by-step explanation:

Choose the correct equation for the graph shown below

Answers

Answer:

the second option, y=1/2cos(x- pi/4)

Step-by-step explanation:

Chris rents a car for a total of £375. The rental charges are £150 for the first day and £75 per day after that. For how many days did Chris rent the car? You must show your working.
I have attempted the question (see picture), but I've only managed to get 2/3 marks!!! Please help! (I will award brainliest btw) TIA ;-)​

Answers

9514 1404 393

Answer:

  4 days

Step-by-step explanation:

The total charges can be modeled by ...

  c = 75d + 75 . . . . . . charges for d days

Filling in the given charge, we find ...

  375 = 75d +75

  300 = 75d . . . . . . . subtract 75

  4 = d . . . . . . . . . . divide by 75

Chris rented the car for 4 days.

Answer:

4 DAYS!! THIS GETS ALL 3 MARKS!!!

Step-by-step explanation:

COPY AND PASTE THIS I USED IT EVEN THO ITS LONG <333 IT GETS THE 3 MARKS

Chris rents a car for a total of £375. The rental charges are £150 for the first day and £75 per day after that. For how many days did Chris rent the car? You must show your working.

£375.00 - £150.00 = £225.00

£225.00 - £75.00 = £150.00

£150.00 - £75.00 = £75.00

£75.00 - £75.00 = £00.00

= Chris rented the car for 4 days

225.00 ÷ 75 = 3

3 days + 1 days = 4 days

he total charges can be modeled by ...

c = 75d + 75 . . . . . . charges for d days

Filling in the given charge, we find ...

375 = 75d +75

300 = 75d . . . . . . . subtract 75

4 = d . . . . . . . . . . divide by 75

Answer:4 days

Total=375

150+(75×4)=150+75+75+75=375

4 days

1. Shoe B was created by rotating Shoe A counterclockwise about a fixed point. How many degrees was the shoe rotated?

Answers

Answer:

90°

Step-by-step explanation:

Rotation counterclockwise means the rotating an object over a fixed point in the opposite direction of our normal wall clock.

To get exact position of shoe B, shoe A would be rotated in about 90° in the opposite direction of a clock.

Thus, shoe A was rotated 90° about a fixed point to create shoe B.

Completing the Square
2. Solve the equation by completing the square. Show your work.
x2 – 30x = –125
Step 1: Add (b/2)^2 to both sides of the equation. (2 points)


Step 2: Factor the left side of the equation. Show your work. (2 points)
Hint: It is a perfect square trinomial.



Step 3: Take the square root of both sides of the equation from Step 2. (1 point)


Step 4: Simplify the radical and solve for x. Show your work. (1 point)

Answers

Answer:

See below

Step-by-step explanation:

Step 1

x^2 – 30x = –125

-30/2 = -15

(-15)^2 = 225

Step 2

x^2 -30x+225 = -125+225

(x-15)^2 = 100

Step 3

Take the square root of each side

sqrt((x-15)^2) = sqrt(100)

Step 4

x-15 = ±10

x-15 =10    x-15 = -10

x= 10+15    x = -10 +15

x = 25      x = 5

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Sometimes preoccuniad with The stock brokerage firm of Blank, Leibowitz, and Webber has analyzed and recommended two stocks to an investor. The investor was interested in factors such as short-term growth, intermediate growth, and dividends rates. The data on each stock is as follows: STOCK ($) FACTOR LOUISIANA GAS AND POWER TRIMEX INSULATION COMPANY Short-term growth potential, per dollar invested 0.36 0.24 Intermediate growth potential (over next 3 years), per dollar invested 1.80 1.50 Dividend rate potential 4% 8%The investor has the following goals: an appreciation of no less than $720 in the short term, an appreciation of at least $5000 in the next three years, and a dividend income of at least $200 per year. What is the smallest investment the investor can make to meet these three goals. 2. 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