What is (1/a-9/(a^2)+(20)/(a^3)}{\frac{16)/a-a} ?

The solution to (1/a-9/(a^2)+(20)/(a^3)}{\frac{16)/a-a} is -(a-5)/(a^2(a+4))

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simplify (1/a-9/(a^2)+(20)/(a^3)}{\frac{16)/a-a}

simplify

\frac{\frac{1}{a} - \frac{9}{a ^{2}} + \frac{20}{a ^{3}}}{\frac{16}{a} - a}

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

Solution steps

\frac{\frac{1}{a} - \frac{9}{a ^{2}} + \frac{20}{a ^{3}}}{\frac{16}{a} - a}

Join

\frac{1}{a} - \frac{9}{a ^{2}} + \frac{20}{a ^{3}} : \frac{a ^{2} - 9 a + 20}{a ^{3}}

= \frac{\frac{a ^{2} - 9 a + 20}{a ^{3}}}{\frac{16}{a} - a}

Join

\frac{16}{a} - a : \frac{- a ^{2} + 16}{a}

= \frac{\frac{a ^{2} - 9 a + 20}{a ^{3}}}{\frac{- a ^{2} + 16}{a}}

Apply the fraction rule:

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

= \frac{( a ^{2} - 9 a + 20 ) a}{a ^{3} ( - a ^{2} + 16 )}

Cancel

\frac{( a ^{2} - 9 a + 20 ) a}{a ^{3} ( - a ^{2} + 16 )} : - \frac{a - 5}{a ^{2} ( a + 4 )}

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

(- 8 x)^{- 2}

8 3^{2}

\frac{\frac{3 y + 2}{3 y}}{\frac{6 y ^{2} + 4 y}{3 y + 2}}

(\frac{x ^{2} + 4 x}{2 x + 6}) (\frac{2 x + 4}{x + 4})

- \frac{1}{x} - 1

What is (1/a-9/(a^2)+(20)/(a^3)}{\frac{16)/a-a} ?
The solution to (1/a-9/(a^2)+(20)/(a^3)}{\frac{16)/a-a} is -(a-5)/(a^2(a+4))