Simplify: (3^ -1 +6^ -1 ) (3 4 )^ -1 - Vidyadip

Question

Simplify: $\big(3^{-1}+6^{-1}\big)\div\Big(\frac{3}{4}\Big)^{-1}$

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Answer

$\big(3^{-1}+6^{-1}\big)\div\Big(\frac{3}{4}\Big)^{-1}$
$=\Big(\frac{1}{3}+\frac{1}{6}\Big)\div\Big(\frac{4}{3}\Big)^1$
$=\bigg(\Big[\frac{1\times2}{3\times2}\Big]+\Big[\frac{1\times1}{6\times1}\Big]\bigg)\div\Big(\frac{4}{3}\Big)$
$=\Big(\frac{2+1}{6}\Big)\div\Big(\frac{4}{3}\Big)$
$=\Big(\frac{3}{6}\Big)\div\Big(\frac{4}{3}\Big)$
$=\Big(\frac{1}{2}\Big)\div\Big(\frac{4}{3}\Big)$
$=\Big(\frac{1}{2}\Big)\times\Big(\frac{3}{4}\Big)$
$=\Big(\frac{3}{8}\Big)$
$\therefore\big(3^{-1}+6^{-1}\big)\div\Big(\frac{3}{4}\Big)^{-1}=\frac{3}{8}$

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