Question

Simplify the complex rational expression by LCD:

$\frac{{\displaystyle \frac{1}{4}}+{\displaystyle \frac{3}{8}}}{{\displaystyle \frac{1}{2}}-{\displaystyle \frac{5}{16}}}$

Short answer

$\frac{10}{3}$

Step-by-step solution

Step 1. Given information.

The following complex rational expression is given:

$\frac{{\displaystyle \frac{1}{4}+\frac{3}{8}}}{{\displaystyle \frac{1}{2}-\frac{5}{16}}}$

Step 2. Simplification of the rational expression.

The LCD of all the fractions in the whole expression is 16.

Multiply both the numerator and the denominator by 16:

$\frac{{\displaystyle 16\left(\frac{1}{4}+\frac{3}{8}\right)}}{{\displaystyle 16\left(\frac{1}{2}-\frac{5}{16}\right)}}$

Distribute:

$\frac{{\displaystyle 16·\frac{1}{4}+16·\frac{3}{8}}}{{\displaystyle 16·\frac{1}{2}-16·\frac{5}{16}}}$

Simplify:

$$\begin{gathered} \frac{{\displaystyle 4+6}}{{\displaystyle 8-5}} \\ \frac{10}{3} \end{gathered}$$