3 years ago

P+1/p=7 then p^3+1/p^3

Mathematics

1 answer:

arlik [135]3 years ago

4 0

This is your perfect answer

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What is the partial fraction decomposition of StartFraction 8 x + 19 Over (x + 8) (x minus 1) EndFraction? StartFraction 3 Over

hoa [83]

The partial fraction decomposition is $\frac{8x + 19}{(x + 8)(x - 1)} = \frac{5}{x + 8} + \frac{3}{x - 1}$

<h3>How to determine the decomposition?</h3>

The fraction is given as:

$\frac{8x + 19}{(x + 8)(x - 1)}$

Split the fraction as follows:

$\frac{8x + 19}{(x + 8)(x - 1)} = \frac{A}{x + 8} + \frac{B}{x - 1}$

Take the LCM

$\frac{8x + 19}{(x + 8)(x - 1)} = \frac{Ax -A + Bx + 8B}{(x + 8)(x -1)}$

Cancel the common factors

8x + 19 = Ax - A + Bx + 8B

By comparison, we have:

Ax + Bx = 8x

-A + 8B = 19

This gives

A + B = 8

-A + 8B = 19

Add both equations

9B = 27

Divide by 9

B = 3

Substitute B = 3 in A + B = 8

A + 3 = 8

Solve for A

A = 5

So, we have:

$\frac{8x + 19}{(x + 8)(x - 1)} = \frac{5}{x + 8} + \frac{3}{x - 1}$

Hence, the partial fraction decomposition is $\frac{8x + 19}{(x + 8)(x - 1)} = \frac{5}{x + 8} + \frac{3}{x - 1}$

Read more about partial fraction at:

brainly.com/question/12783868

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