Question

Simplify a Complex Rational Expression by Using the LCD.

In the following exercises, simplify.

$\frac{\frac{1}{6}+\frac{4}{15}}{\frac{3}{5}-\frac{1}{2}}$

Short answer

The simplified form of the given expression is $\frac{13}{3}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\frac{\frac{1}{6}+\frac{4}{15}}{\frac{3}{5}-\frac{1}{2}}$

Step 2. Rewrite the expression and then simplify.

The LCD of all the fractions in the whole expression is 30. Clear the fractions by multiplying the numerator and denominator by that LCD.

$$\begin{gathered} =\frac{30·\left(\frac{1}{6}+\frac{4}{15}\right)}{30·\left(\frac{3}{5}-\frac{1}{2}\right)} \\ =\frac{30·\frac{1}{6}+30·\frac{4}{15}}{30·\frac{3}{5}-30·\frac{1}{2}} \\ =\frac{5+8}{18-15} \\ =\frac{13}{3} \end{gathered}$$

Step 3. Conclusion.

The simplified form of the given expression is $\frac{13}{3}$.