# How do you simplify 6x^2 - 7x + 2 div 6x^2 + 5x - 6?

Aug 20, 2017

$\frac{2 x - 1}{2 x + 3}$

#### Explanation:

Given $6 {x}^{2} - 7 x + 2 \div 6 {x}^{2} + 5 x - 6$

$\Rightarrow \frac{6 {x}^{2} - \left(4 + 3\right) x + 2}{6 {x}^{2} + \left(9 - 4\right) x - 6}$

$\Rightarrow \frac{6 {x}^{2} - 4 x - 3 x + 2}{6 {x}^{2} + 9 x - 4 x - 6}$

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

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

$\Rightarrow \frac{2 x - 1}{2 x + 3}$