Question

Simplify$\frac{2}{\frac{1}{3}+\frac{1}{5}}$

Short answer

On simplifying the given expression, we get

$\frac{2}{\frac{1}{3}+\frac{1}{5}}=\frac{15}{4}$

Step-by-step solution

Step 1. Given information 

$\begin{array}{l}\text{Theexpressiongivenis}\\ \frac{2}{\frac{1}{3}+\frac{1}{5}}\\ \text{Wehavetosimplifythegivenexpression}\end{array}$

Step 2. Simplify the numerator and denominator 

$\begin{array}{l}\Rightarrow \frac{2}{\frac{1}{3}+\frac{1}{5}}=\frac{2}{\left(\frac{3+5}{3\times 5}\right)}\left[\text{TaketheLCMindenominator}\right]\\ \Rightarrow \frac{2}{\frac{1}{3}+\frac{1}{5}}=\frac{2}{\left(\frac{8}{15}\right)}\end{array}$

Step 3. Simplify the fraction 

$\begin{array}{l}\Rightarrow \frac{2}{\frac{1}{3}+\frac{1}{5}}=\frac{2}{\left(\frac{8}{15}\right)}\\ \Rightarrow \frac{2}{\frac{1}{3}+\frac{1}{5}}=\frac{2\times 15}{8}\\ \Rightarrow \frac{2}{\frac{1}{3}+\frac{1}{5}}=\frac{\cancel{2}\times 15}{\cancel{2}\times 4}\\ \Rightarrow \frac{2}{\frac{1}{3}+\frac{1}{5}}=\frac{15}{4}\end{array}$