# How do you divide 2x^2-5x-3 by 2x-6 ?

Mar 4, 2017

$\frac{2 {x}^{2} - 5 x - 3}{2 x - 6} = x + \frac{1}{2}$

#### Explanation:

We can split the numerator up into parts which are monomial multiples of $\left(2 x - 6\right)$, then combine them like this:

$\frac{2 {x}^{2} - 5 x - 3}{2 x - 6} = \frac{2 {x}^{2} - 6 x + x - 3}{2 x - 6}$

$\textcolor{w h i t e}{\frac{2 {x}^{2} - 5 x - 3}{2 x - 6}} = \frac{x \left(2 x - 6\right) + \frac{1}{2} \left(2 x - 6\right)}{2 x - 6}$

$\textcolor{w h i t e}{\frac{2 {x}^{2} - 5 x - 3}{2 x - 6}} = \frac{\left(x + \frac{1}{2}\right) \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(2 x - 6\right)}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(2 x - 6\right)}}}}$

$\textcolor{w h i t e}{\frac{2 {x}^{2} - 5 x - 3}{2 x - 6}} = x + \frac{1}{2}$