Question

If $\{{\left(\frac{3}{4}\right)}^{-1}-{\left(\frac{1}{4}\right)}^{-1}\}=$ $-\frac{3}{m}$, the the value of $m$ is

Answer 1

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

$={(\frac{4}{3}-\frac{4}{1})}^{-1}$

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

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

$=\frac{1}{-8/3}=\frac{3}{-8}=-\frac{3}{8}$