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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Updated on: 10-Oct-2022

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