What is (\frac{a-4)/(a^2-2a-8)}{1/(a-5)} ?

The solution to (\frac{a-4)/(a^2-2a-8)}{1/(a-5)} is (a-5)/(a+2)

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simplify (\frac{a-4)/(a^2-2a-8)}{1/(a-5)}

simplify

\frac{\frac{a - 4}{a ^{2} - 2 a - 8}}{\frac{1}{a - 5}}

\frac{a - 5}{a + 2}

Solution steps

\frac{\frac{a - 4}{a ^{2} - 2 a - 8}}{\frac{1}{a - 5}}

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{( a - 4 ) ( a - 5 )}{( a ^{2} - 2 a - 8 ) \cdot 1}

Apply rule:

a \cdot 1 = a

= \frac{( a - 4 ) ( a - 5 )}{a ^{2} - 2 a - 8}

Cancel

\frac{( a - 4 ) ( a - 5 )}{a ^{2} - 2 a - 8} : \frac{a - 5}{a + 2}

= \frac{a - 5}{a + 2}

(x^{3} + 2)^{3}

6 - \frac{1}{2} (4 (x - 3)^{2})

0. 3^{12}

(5 x + 4 y)^{3}

- 0.5 lo g_{2} (0.5) - 0.5 lo g_{2} (0.5)

What is (\frac{a-4)/(a^2-2a-8)}{1/(a-5)} ?
The solution to (\frac{a-4)/(a^2-2a-8)}{1/(a-5)} is (a-5)/(a+2)