The value of $\left( 7^{-1} \ -\ 8^{-1}\right)^{-1} -\ \left( 3^{-1} \ -\ 4^{-1}\right)^{-1}$ is:

(a) 44 (b) 56 (c) 68 (d) 12

Given: $\left( 7^{-1} \ -\ 8^{-1}\right)^{-1} -\ \left( 3^{-1} \ -\ 4^{-1}\right)^{-1}$

To find: Here we have to find the value of $\left( 7^{-1} \ -\ 8^{-1}\right)^{-1} -\ \left( 3^{-1} \ -\ 4^{-1}\right)^{-1}$.

Solution:

$\left( 7^{-1} \ -\ 8^{-1}\right)^{-1} -\ \left( 3^{-1} \ -\ 4^{-1}\right)^{-1}$

$=\ \left(\frac{1}{7} \ -\ \frac{1}{8}\right)^{-1} -\ \left(\frac{1}{3} \ -\ \frac{1}{4}\right)^{-1}$

$=\ \left(\frac{8\ -\ 7}{56}\right)^{-1} -\ \left(\frac{4\ -\ 3}{12}\right)^{-1}$

$=\ \left(\frac{1}{56}\right)^{-1} -\ \left(\frac{1}{12}\right)^{-1}$

$=\ 56\ -\ 12$

$=\ \mathbf{44}$

So, value of the given expression is 44.

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Updated on: 10-Oct-2022

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