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Solve the following
$\left\{\left(\frac{-5}{2}\right)^{-1} -\ \left(\frac{-1}{2}\right)^{-1}\right\}^{-1}$
Given:$\left\{\left(\frac{-5}{2}\right)^{-1} -\ \left(\frac{-1}{2}\right)^{-1}\right\}^{-1}$
To Do: Solve the given expression
Solution:
$\left(\frac{-5}{2}\right)^{-1}$ = $\frac{2}{5}$ [-1 in power means, reciprocal ]
=$\ \left(\frac{-1}{2}\right)^{-1}$ = 2
=$\frac{2}{5} -2$
5 is LCM.
=$\left(\frac{2}{5} -\frac{2\times 5}{5}\right)$
$ \begin{array}{l}
=\left(\frac{2}{5} -\frac{10}{5}\right)\
=\left(\frac{2-10}{5}\right)\
=\left(\frac{-8}{5}\right)
\end{array}$
Therefore $\left\{\left(\frac{-5}{2}\right)^{-1} -\ \left(\frac{-1}{2}\right)^{-1}\right\}^{-1}$ = $\frac-{5}{8}$
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