What is (5x-40)/(64-x^2) ?

The solution to (5x-40)/(64-x^2) is -5/(8+x)

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simplify (5x-40)/(64-x^2)

simplify

\frac{5 x - 40}{64 - x ^{2}}

- \frac{5}{8 + x}

Solution steps

\frac{5 x - 40}{64 - x ^{2}}

Factor

5 x - 40 : 5 (x - 8)

= \frac{5 ( x - 8 )}{64 - x ^{2}}

Factor

64 - x^{2} : (8 + x) (8 - x)

= \frac{5 ( x - 8 )}{( 8 + x ) ( 8 - x )}

(8 + x) (8 - x) = - (8 + x) (x - 8)

= \frac{5 ( x - 8 )}{- ( 8 + x ) ( x - 8 )}

Cancel the common factor:

x - 8

= \frac{5}{- ( 8 + x )}

Apply the fraction rule:

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

= - \frac{5}{8 + x}

Γ (\frac{5}{3})

- 9 - - 98 - 16 + - 8

23 \times 38

\frac{x ^{2} + 13 x + 40}{x ^{2} + 9 x + 20}

6 x^{2} - 19 x + 14