Question

In the following exercise, simplify $\frac{{\displaystyle \frac{2}{5}}+{\displaystyle \frac{5}{6}}}{{\displaystyle \frac{1}{3}}+{\displaystyle \frac{1}{4}}}$

Short answer

The solution is$\frac{74}{35}$

Step-by-step solution

Step 1. Given Information

$\frac{{\displaystyle \frac{2}{5}+\frac{5}{6}}}{{\displaystyle \frac{1}{3}+\frac{1}{4}}}$

Step 2. Simplify

Simplify the numerator and denominator.

Find the LCD and add the fractions in the numerator.

Find the LCD and subtract the fractions in the denominator.

$$\begin{gathered} =\frac{{\displaystyle \frac{12+25}{30}}}{{\displaystyle \frac{4+3}{12}}} \\ =\frac{37}{{\displaystyle \frac{30}{{\displaystyle \frac{7}{12}}}}} \end{gathered}$$

Rewrite the complex rational expression as a division problem.

$=\frac{37}{30}÷\frac{7}{12}$

Multiply the first by the reciprocal of the second.

$$\begin{gathered} =\frac{37}{30}\times \frac{12}{7} \\ =\frac{74}{35} \end{gathered}$$