What is (x+5)/(x^2-2x-15)-1/(x-5) ?

The solution to (x+5)/(x^2-2x-15)-1/(x-5) is 2/((x+3)(x-5))

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simplify (x+5)/(x^2-2x-15)-1/(x-5)

simplify

\frac{x + 5}{x ^{2} - 2 x - 15} - \frac{1}{x - 5}

\frac{2}{( x + 3 ) ( x - 5 )}

Solution steps

\frac{x + 5}{x ^{2} - 2 x - 15} - \frac{1}{x - 5}

Least Common Multiplier of

x^{2} - 2 x - 15, x - 5 : (x + 3) (x - 5)

Adjust Fractions based on the LCM

= \frac{x + 5}{( x + 3 ) ( x - 5 )} - \frac{x + 3}{( x + 3 ) ( x - 5 )}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{x + 5 - ( x + 3 )}{( x + 3 ) ( x - 5 )}

Simplify

x + 5 - (x + 3) : 2

= \frac{2}{( x + 3 ) ( x - 5 )}

(x - 6) (x + 8)

- 2 - x

- x - 3

11 - 4

14 - 5

What is (x+5)/(x^2-2x-15)-1/(x-5) ?
The solution to (x+5)/(x^2-2x-15)-1/(x-5) is 2/((x+3)(x-5))