What is (a^{-1}+5)/(a^{-1)-5} ?

The solution to (a^{-1}+5)/(a^{-1)-5} is (5a+1)/(-5a+1)

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simplify (a^{-1}+5)/(a^{-1)-5}

simplify

\frac{a ^{- 1} + 5}{a ^{- 1} - 5}

\frac{5 a + 1}{- 5 a + 1}

Solution steps

\frac{a ^{- 1} + 5}{a ^{- 1} - 5}

Simplify

a^{- 1} + 5 : \frac{5 a + 1}{a}

= \frac{\frac{5 a + 1}{a}}{a ^{- 1} - 5}

Simplify

a^{- 1} - 5 : \frac{- 5 a + 1}{a}

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

Apply the fraction rule:

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

= \frac{( 5 a + 1 ) a}{a ( - 5 a + 1 )}

Cancel the common factor:

a

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

\frac{( x ^{2} + 3 x + 2 )}{( x - 4 )} < 0

- 2 x^{2} + 15 x - 7

\frac{4}{7} \cdot 4

- (2 x + 1)^{6}

\frac{3 x ^{8} y ^{3}}{9 x ^{6} y ^{8}}

What is (a^{-1}+5)/(a^{-1)-5} ?
The solution to (a^{-1}+5)/(a^{-1)-5} is (5a+1)/(-5a+1)