Question

Evaluate:

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

• A. $\frac{3}{8}$
• B. $-\frac{3}{8}$
• C. $\frac{8}{3}$
• D. $-\frac{8}{3}$

Answer 1

Answer: (B)

$-\frac{3}{8}$

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

$\Rightarrow {\{\frac{4}{3}-\frac{4}{1}\}}^{-1}$

$\Rightarrow {\left\{\frac{4-12}{3}\right\}}^{-1}$

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

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