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

Oct 10, 2015

#### Answer:

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

#### Explanation:

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

The top is already simplified as far as possible (for now) so let's jump to the bottom instead:

${x}^{2} - 7 x + 6$
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:

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

This is our answer.
Hope this helped!