# How do you multiply (18x-36)/(4x-8)*2/(9x+18) and state the excluded values?

Nov 1, 2016

=$\frac{1}{x + 2}$

$x \ne 2 \mathmr{and} x \ne - 2$

#### Explanation:

$\frac{18 x - 36}{4 x - 8} \cdot \frac{2}{9 x + 18} \text{ } \leftarrow$ factorise first

$= \frac{18 \left(x - 2\right) \times 2}{4 \left(x - 2\right) \times 9 \left(x + 2\right)}$

$= \frac{{\cancel{18}}^{\cancel{2}} \cancel{\left(x - 2\right)} \times \cancel{2}}{\cancel{4} \cancel{\left(x - 2\right)} \times \cancel{9} \left(x + 2\right)} \text{ } \leftarrow$ cancel like factors

$= \frac{1}{x + 2}$

Remember that the denominator may not be zero,
The excluded values are therefore the values which
would give us 0.