# How do you simplify (3x-8)/(6x^2-16x) and then find the excluded values?

Jul 21, 2017

$\frac{1}{2 x} , x \ne 0$

#### Explanation:

$\text{simplify thedenominator by factorising}$

$\frac{3 x - 8}{2 x \left(3 x - 8\right)} \leftarrow \textcolor{b l u e}{\text{ common factor of 2x}}$

$\text{cancel the common factor } \left(3 x - 8\right)$

$\frac{\cancel{\left(3 x - 8\right)}}{2 x \cancel{\left(3 x - 8\right)}} = \frac{1}{2 x}$

$\Rightarrow \frac{3 x - 8}{6 {x}^{2} - 16 x}$

$= \frac{1}{2 x} \to x \ne 0 \leftarrow \textcolor{red}{\text{ excluded value}}$