Evaluate: (3 5 12 +1 2 3 ) (3 5 12 -1 2 3 ) - Vidyadip

Question

Evaluate: $\left(3 \frac{5}{12}+1 \frac{2}{3}\right) \div\left(3 \frac{5}{12}-1 \frac{2}{3}\right)$

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Answer

$\begin{aligned} & \left(3 \frac{5}{12}+1 \frac{2}{3}\right) \div\left(3 \frac{5}{12}-1 \frac{2}{3}\right) \\ & =\left(\frac{12 \times 3+5}{12}+\frac{3 \times 1+2}{3}\right) \div\left(\frac{12 \times 3+5}{12}-\frac{3 \times 1+2}{3}\right) \\ & =\left(\frac{41}{12}+\frac{5}{3}\right) \div\left(\frac{41}{12}-\frac{5}{3}\right) \\ & (\because \text { L.C.M. of } 12,3=12) \\ & =\left(\frac{41+20}{12}\right) \div\left(\frac{41-20}{12}\right) \\ & =\frac{61}{12} \div \frac{21}{12} \Rightarrow \frac{61}{12} \times \frac{12}{21} \\ & =\frac{61}{21}=2 \frac{19}{21}\end{aligned}$

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