# How do you simplify (x-6)/(x^2-7x+6)?

Oct 10, 2015

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

#### Explanation:

This equation can be separated into two parts, the top and the bottom, which we can simplify further.

${x}^{2} - 7 x + 6$
This can be factored into the following:
$\left(x - 6\right) \left(x - 1\right)$
-6 and -1 both add to equal -7, and multiplied they equal 6, fitting the polynomial.

From here we can cancel an $\left(x - 6\right)$ from the top and bottom:

$\frac{x - 6}{\left(x - 6\right) \left(x - 1\right)}$
$\frac{\cancel{x - 6}}{\cancel{x - 6} \left(x - 1\right)}$
$\frac{1}{x - 1}$