# How do you simplify x/(x-3)-3/(x+2)?

Apr 8, 2017

$\frac{{x}^{2} - x + 9}{\left(x - 3\right) \left(x + 2\right)}$

#### Explanation:

Before we can subtract fractions we require them to have a $\textcolor{b l u e}{\text{common denominator}}$

To obtain a common denominator for both fractions.

• "multiply numerator/denominator of " x/(x-3)" by " (x+2)

•"multiply numerator/denominator of " 3/(x+2)"by " (x-3)

$\Rightarrow \frac{x \textcolor{red}{\left(x + 2\right)}}{\left(x - 3\right) \textcolor{red}{\left(x + 2\right)}} - \frac{3 \textcolor{red}{\left(x - 3\right)}}{\textcolor{red}{\left(x - 3\right)} \left(x + 2\right)}$

Now there is a common denominator, subtract the numerators leaving the denominator as it is.

$= \frac{x \left(x + 2\right) - 3 \left(x - 3\right)}{\left(x - 3\right) \left(x + 2\right)}$

distribute the numerator and simplify.

$= \frac{{x}^{2} + 2 x - 3 x + 9}{\left(x - 3\right) \left(x + 2\right)}$

$= \frac{{x}^{2} - x + 9}{\left(x - 3\right) \left(x + 2\right)}$