# What is the LCD of \frac { x + 5} { 4x - 12} - \frac { 2} { x - 3}?

May 14, 2017

See solution explanation below:

#### Explanation:

Multiply the fraction on the right by $\textcolor{red}{\frac{4}{4}}$:

$\frac{4}{4} \times \frac{2}{x - 3} \implies \frac{\textcolor{red}{4} \cdot 2}{\textcolor{red}{4} \left(x - 3\right)} \implies \frac{8}{\left(\textcolor{red}{4} \cdot x\right) - \left(\textcolor{red}{4} \cdot 3\right)} \implies$

$\frac{8}{4 x - 12}$

Therefore the LCD (Lowest Common Denominator) is: $4 x - 12$

and the expression can be rewritten as:

$\frac{x + 5}{4 x - 12} - \frac{8}{4 x - 12}$