# How do you subtract (3x+1)/(2x) - (x+1)/(x-3)?

Apr 11, 2017

$\frac{{x}^{2} - 10 x - 3}{2 x \left(x - 3\right)}$

#### Explanation:

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

To obtain this.

$\text{multiply numerator/denominator of " (3x+1)/(2x)" by } \left(x - 3\right)$

$\text{multiply numerator/denominator of " (x+1)/(x-3)" by } 2 x$

$\Rightarrow \frac{\left(3 x + 1\right) \left(\textcolor{red}{x - 3}\right)}{2 x \left(\textcolor{red}{x - 3}\right)} - \frac{\textcolor{m a \ge n t a}{2 x} \left(x + 1\right)}{\textcolor{m a \ge n t a}{2 x} \left(x - 3\right)}$

The fractions now have a common denominator so we can subtract the numerators while leaving the denominator.

$= \frac{\left(3 x + 1\right) \left(x - 3\right) - 2 x \left(x + 1\right)}{2 x \left(x - 3\right)}$

distributing the numerator and simplifying gives.

$= \frac{3 {x}^{2} - 8 x - 3 - 2 {x}^{2} - 2 x}{2 x \left(x - 3\right)}$

$= \frac{{x}^{2} - 10 x - 3}{2 x \left(x - 3\right)}$