# How do you factor (x^2-14x+49)/(x^2-2x-35)?

Jun 30, 2016

$\frac{x - 7}{x + 5}$

#### Explanation:

The numerator is a squared bynomial:

${x}^{2} - 14 x + 49 = {\left(x - 7\right)}^{2}$

the denominator is similar to a trynomial of the type

${x}^{2} + s x + p$

where you can find two numbers whose sum is s and whose product is p, in this case the numbers are -7 and 5 because

-7+5=-2 and -7*5=-35

so

${x}^{2} - 2 x - 35 = \left(x - 7\right) \left(x + 5\right)$

now you can rewrite the fraction:

${\left(x - 7\right)}^{\cancel{2}} / \left(\cancel{x - 7} \left(x + 5\right)\right)$