Question

Simplify the complex rational expression by LCD:

$\frac{{\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{5}}}{{\displaystyle \frac{1}{10}}+{\displaystyle \frac{1}{5}}}$

Short answer

$\frac{7}{3}$

Step-by-step solution

Step 1. Given information.

The following complex rational expression is given:

$\frac{{\displaystyle \frac{1}{2}+\frac{1}{5}}}{{\displaystyle \frac{1}{10}+\frac{1}{5}}}$

Step 2. Simplification of the complex rational expression.

The LCD of all the fractions in the whole expression is 10.

Clear the fraction by multiplying the numerator and the denominator by the LCD i.e., 10:

$\frac{{\displaystyle 10.\left(\frac{1}{2}+\frac{1}{5}\right)}}{{\displaystyle 10.\left(\frac{1}{10}+\frac{1}{5}\right)}}$

Distribute:

$\frac{{\displaystyle 10.\frac{1}{2}+10.\frac{1}{5}}}{{\displaystyle 10.\frac{1}{10}+10.\frac{1}{5}}}$

Simplify:

role="math" localid="1644719678072" $$\begin{gathered} \frac{{\displaystyle 5+2}}{{\displaystyle 1+2}} \\ \frac{7}{3} \end{gathered}$$