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

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

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

simplify

\frac{( a ^{2} - 1 ) ^{- 1}}{( a - 1 ) ^{- 1}}

\frac{1}{a + 1}

Solution steps

\frac{( a ^{2} - 1 ) ^{- 1}}{( a - 1 ) ^{- 1}}

Factor

(a^{2} - 1)^{- 1} : (a + 1)^{- 1} (a - 1)^{- 1}

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

Cancel the common factor:

(a - 1)^{- 1}

= (a + 1)^{- 1}

Apply exponent rule:

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

= \frac{1}{a + 1}

\frac{x ^{2} ( x + 4 )}{( x - 1 ) ( x + 2 )} > 0

\frac{8 ^{5}}{8}

(3 x^{- 2} y^{4})^{- 3}

5 \leq 5 t - 5 \leq 20

3 x^{2} - 4 x - 4 = 2 x^{2} - 12 x

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