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Evaluate : $\left(2^{-1}-3^{-1}\right)^{-1}+\left(6^{-1}-8^{-1}\right)^{-1}$
To do : We have to simplify $\left(2^{-1}-3^{-1}\right)^{-1}+\left(6^{-1}-8^{-1}\right)^{-1}$
First term : $\left(2^{-1}-3^{-1}\right)^{-1}$
Apply exponent rule: $\quad a^{-1}=\frac{1}{a}$
$=\left(\frac{1}{2}-\frac{1}{3}\right)^{-1}$
Join $\frac{1}{2}-\frac{1}{3}: \frac{1}{6}$
$=\left(\frac{1}{6}\right)^{-1}$
Apply exponent rule: $\quad a^{-1}=\frac{1}{a}$
$=\frac{1}{\frac{1}{6}}$
Apply the fraction rule: $\quad \frac{1}{\frac{b}{c}}=\frac{c}{b}$
$=\frac{6}{1}$
$=6$
Similarly we can simplify second term as $\left(6^{-1}-8^{-1}\right)^{-1}=24$
Adding both terms:
$=6+24$
$=30$
Updated on: 10-Oct-2022
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