How do you simplify 3 / (x^2 - 5x + 6) *( x - 3 )/ (x - 2)?

May 17, 2018

$\frac{3}{x - 2} ^ 2$

Explanation:

$\text{factorise the denominator } {x}^{2} - 5 x + 6$

$\text{the factors of + 6 which sum to - 5 are - 2 and - 3}$

$\Rightarrow {x}^{2} - 5 x + 6 = \left(x - 2\right) \left(x - 3\right)$

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

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

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

$= \frac{3}{x - 2} ^ 2$

$\text{with restriction } x \ne 2$