Question

Find the partial fraction decomposition of 2x-5/x^2+3x-10

Answer 1

`(-1)/(7(x-2))+(15)/(7(x+5))`

Explanation:

For f(x) = (2x-5)/((x -2)(x +5)), the decomposition will be of the form ...

f(x) = A/(x -2) +B/(x +5)

The values of A and B can be found from ...

A = (x -2)f(x) evaluated at x=2

A = (2·2-5)/(2+5) = -1/7

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B = (x +5)f(x) evaluated at x=-5

B = (2(-5) -5)/(-5-2) = -15/-7 = 15/7

`(2x-5)/(x^2+3x-10)=\bf{(-1)/(7(x-2))+(15)/(7(x+5))}`