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3 years ago

Which expression is equivalent to x2 − x − 6 x2 + 2x − 15 ? A) x + 3 x + 5 B) x + 2 x + 5 C) x + 3 x − 3 D) x + 2 x − 3

Mathematics

2 answers:

FinnZ [79.3K]3 years ago

7 0

Answer:

D. x + 1 −

x − 3

(usateatprep)

Step-by-step explanation:

x2 − 2x − 5

x − 3

x +

x − 5

x − 3

x + 1 +

−2

x − 3

x + 1 −

x − 3

Tema [17]3 years ago

4 0

Answer:

Well, I am not sure which one is equivalent to another, but I have some information that should help you find your answer.

Step-by-step explanation:

The simplified expression to x2 − x − 6 x2 + 2x − 15 would be equal to −5 x 2 + x − 15.

The simplified expression to x + 3 x + 5 would be equal to 4x + 5.

The simplified expression to x + 2x + 5 would be equal to 3x + 5.

The simplified expression x + 3 x − 3 would be equal to 4x − 3.

The last simplified expression to x + 2 x − 3 would be equal to 3x − 3.

Hope this helps, I am really sorry if I didn't answer your question properly, or the way you asked!

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1. Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.

german

Answer:

Step-by-step explanation:

To write the form of the partial fraction decomposition of the rational expression:

We have:

$\mathbf{\dfrac{8x-4}{x(x^2+1)^2}= \dfrac{A}{x}+\dfrac{Bx+C}{x^2+1}+\dfrac{Dx+E}{(x^2+1)^2}}$

Using partial fraction decomposition to find the definite integral of:

$\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}dx$

By using the long division method; we have:

$x^2-8x-20 | \dfrac{2x}{2x^3-16x^2-39x+20 }$

$- 2x^3 -16x^2-40x$

$x+ 20$

So;

$\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x+\dfrac{x+20}{x^2-8x-20}$

By using partial fraction decomposition:

$\dfrac{x+20}{(x-10)(x+2)}= \dfrac{A}{x-10}+\dfrac{B}{x+2}$

$= \dfrac{A(x+2)+B(x-10)}{(x-10)(x+2)}$

x + 20 = A(x + 2) + B(x - 10)

x + 20 = (A + B)x + (2A - 10B)

Now; we have to relate like terms on both sides; we have:

A + B = 1 ; 2A - 10 B = 20

By solvong the expressions above; we have:

$A = \dfrac{5}{2}$ $B = \dfrac{3}{2}$

Now;

$\dfrac{x+20}{(x-10)(x+2)} = \dfrac{5}{2(x-10)} + \dfrac{3}{2(x+2)}$

Thus;

$\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)}$

Now; the integral is:

$\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx = \int \begin {bmatrix} 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)} \end {bmatrix} \ dx$

$\mathbf{\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx = x^2 + \dfrac{5}{2}In | x-10|\dfrac{3}{2} In |x+2|+C}$

3. Due to the fact that the maximum words this text box can contain are 5000 words, we decided to write the solution for question 3 and upload it in an image format.

Please check to the attached image below for the solution to question number 3.

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Alenkasestr [34]

Answer:

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Step-by-step explanation:

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2 years ago

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MariettaO [177]

Answer:

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Step-by-Step Solution:

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2 years ago

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olasank [31]

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I hope that helped!

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