What is (5-x)/(x^2-25) ?

The solution to (5-x)/(x^2-25) is -1/(x+5)

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simplify (5-x)/(x^2-25)

simplify

\frac{5 - x}{x ^{2} - 25}

- \frac{1}{x + 5}

Solution steps

\frac{5 - x}{x ^{2} - 25}

Factor

x^{2} - 25 : (x + 5) (x - 5)

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

5 - x = - (x - 5)

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

Cancel the common factor:

x - 5

= \frac{- 1}{x + 5}

Apply the fraction rule:

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

= - \frac{1}{x + 5}

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