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const2013 [10]
2 years ago
12

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

x + 8 EndFraction + StartFraction 5 Over x minus 1 EndFraction StartFraction 5 Over x + 8 EndFraction + StartFraction 3 Over x minus 1 EndFraction StartFraction negative 3 Over x + 8 EndFraction + StartFraction 11 Over x minus 1 EndFraction StartFraction 11 Over x + 8 EndFraction + StartFraction negative 3 Over x minus 1 EndFraction
Mathematics
1 answer:
hoa [83]2 years ago
6 0

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

#SPJ1

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