Question

In the following exercise, simplify.

$\frac{{\displaystyle \frac{1}{3}}+{\displaystyle \frac{1}{8}}}{{\displaystyle \frac{1}{4}}+{\displaystyle \frac{1}{12}}}$

Short answer

The solution is$\frac{11}{8}$

Step-by-step solution

Step 1. Given information

$\frac{{\displaystyle \frac{1}{3}+\frac{1}{8}}}{{\displaystyle \frac{1}{4}+\frac{1}{12}}}$

Step2. Simplify

The LCD of all fractions in the complex rational expression is $24\times 3$.

Multiply the numerator and denominator by the LCD.

role="math" localid="1646724877348" $\frac{\left(24\times 3\right)\left({\displaystyle \frac{1}{3}}+{\displaystyle \frac{1}{8}}\right)}{\left(24\times 3\right)\left({\displaystyle \frac{1}{4}}+{\displaystyle \frac{1}{12}}\right)}$

Distribute in the numerator and denominator and simplify

$$\begin{gathered} =\frac{\left({\displaystyle \left(24\times 3\right)\frac{1}{3}+\left(24\times 3\right)\frac{1}{8}}\right)}{\left({\displaystyle \left(24\times 3\right)\frac{1}{4}+\left(24\times 3\right)\frac{1}{12}}\right)} \\ =\frac{24+9}{18+6} \\ =\frac{11}{8} \end{gathered}$$