# How do you simplify (6w^2+11w-7)/(6w-3) and what are the restrictions?

May 27, 2015

Factor $y = 6 {x}^{2} + 11 x - 7.$
Converted $y ' = {x}^{2} + 11 x - 42$.
Factor pairs of -42 ->(-2, 21)(-3, 14)
Then, p' = -3, and q' = 14
Then, $p = - \frac{3}{6} = - \frac{1}{2}$, and $q = \frac{14}{6} = \frac{7}{3}$
$y = \left(x - \frac{1}{2}\right) \left(x + \frac{7}{3}\right) = \left(2 x - 1\right) \left(3 x - 7\right)$

$f \left(x\right) = \frac{\left(2 x - 1\right) \left(3 x - 7\right)}{3 \left(2 x - 1\right)} = \frac{3 x - 7}{3}$

Restriction: (2x -1) should not be zero or x not 1/2