# How do you simplify the rational expression: (x-3)/(x^2-5x+6)?

Jun 8, 2018

$\frac{1}{x - 2}$

#### Explanation:

Simply the ${x}^{2} - 5 x + 6$ first:

Lets find the factors of ${x}^{2} - 5 x + 6$

$3 \times 2 = 6$ ----> adding them gives $5$ ----> we want adding it gives $- 5$

$- 3 \times - 2 = 6$ ----> adding them gives $- 5$ ---> This is the one.

Re-write the equation as follows:

${x}^{2} - 5 x + 6$

${x}^{2} - 3 x - 2 x + 6$

$x \left(x - 3\right) - 2 \left(x - 3\right)$

$\left(x - 2\right) \left(x - 3\right)$

So now we have;

$\frac{x - 3}{{x}^{2} - 5 x + 6}$ = $\frac{x - 3}{\left(x - 2\right) \left(x - 3\right)}$ = cancel(x-3)/((x-2)cancel((x-3))# = $\frac{1}{x - 2}$

Hence its simplified as:

$\frac{x - 3}{{x}^{2} - 5 x + 6}$ = $\frac{1}{x - 2}$