# How do you simplify the expression and find the excluded values for the rational expression \frac{4x-2}{2x^2+x-1}?

Dec 14, 2014

Since the denominator cannot be zero,

$2 {x}^{2} + x - 1 = \left(2 x - 1\right) \left(x + 1\right) \ne 0$

$\implies \left\{\begin{matrix}2 x - 1 \ne 0 \implies 2 x \ne 1 \implies x \ne \frac{1}{2} \\ x + 1 \ne 0 \implies x \ne - 1\end{matrix}\right.$

Hence, the excluded values are $\frac{1}{2}$ and $- 1$.

I hope that this was helpful.