What is (a^{-1}+2)/(a^{-1)-2} ?

The solution to (a^{-1}+2)/(a^{-1)-2} is (2a+1)/(-2a+1)

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simplify (a^{-1}+2)/(a^{-1)-2}

simplify

\frac{a ^{- 1} + 2}{a ^{- 1} - 2}

\frac{2 a + 1}{- 2 a + 1}

Solution steps

\frac{a ^{- 1} + 2}{a ^{- 1} - 2}

Simplify

a^{- 1} + 2 : \frac{2 a + 1}{a}

= \frac{\frac{2 a + 1}{a}}{a ^{- 1} - 2}

Simplify

a^{- 1} - 2 : \frac{- 2 a + 1}{a}

= \frac{\frac{2 a + 1}{a}}{\frac{- 2 a + 1}{a}}

Apply the fraction rule:

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

= \frac{( 2 a + 1 ) a}{a ( - 2 a + 1 )}

Cancel the common factor:

a

= \frac{2 a + 1}{- 2 a + 1}

\frac{15}{125}

25 (- 8 x^{3} + 3 x^{2} + 6 x)

x^{2} - 6 x = 2

2 y^{2} + 10 y

\frac{1}{1 0 ^{2}}

What is (a^{-1}+2)/(a^{-1)-2} ?
The solution to (a^{-1}+2)/(a^{-1)-2} is (2a+1)/(-2a+1)