Question

Simplify$\frac{5}{\frac{1}{4}+\frac{1}{3}}$

Short answer

On simplifying the given expression, we get

$\frac{5}{\frac{1}{4}+\frac{1}{3}}=\frac{60}{7}$

Step-by-step solution

Step 1. Given information 

$\begin{array}{l}\text{Theexpressiongivenis}\\ \frac{5}{\frac{1}{4}+\frac{1}{3}}\\ \text{Wehavetosimplifythegivenexpression.}\end{array}$

Step 2. Simplify the numerator and denominator 

$\begin{array}{l}\Rightarrow \frac{5}{\frac{1}{4}+\frac{1}{3}}=\frac{5}{\left(\frac{3+4}{4\times 3}\right)}\left[\text{TaketheLCMindenominator}\right]\\ \Rightarrow \frac{5}{\frac{1}{4}+\frac{1}{3}}=\frac{5}{\left(\frac{7}{12}\right)}\end{array}$

Step 3. Simplify the fraction 

$\begin{array}{l}\Rightarrow \frac{5}{\frac{1}{4}+\frac{1}{3}}=\frac{5}{\left(\frac{7}{12}\right)}\\ \Rightarrow \frac{5}{\frac{1}{4}+\frac{1}{3}}=\frac{5\times 12}{7}\\ \Rightarrow \frac{5}{\frac{1}{4}+\frac{1}{3}}=\frac{60}{7}\end{array}$