# How can you evaluate (6x-1)/(x^2-25) - (7x-6)/(x^2-25) ?

Jul 29, 2015

=color(blue)(-1/(x+5)

#### Explanation:

$\frac{6 x - 1}{{x}^{2} - 25} - \frac{7 x - 6}{{x}^{2} - 25}$

Here we can combine the numerators of the two terms as the denominators are equal.

$= \frac{\left(6 x - 1\right) - \left(7 x - 6\right)}{{x}^{2} - 25}$

$= \frac{\left(6 x - 1 - 7 x + 6\right)}{{x}^{2} - 25}$

$= \frac{\left(6 x - 7 x + 6 - 1\right)}{{x}^{2} - 25}$

$= \frac{\left(- x + 5\right)}{{x}^{2} - 25}$

Now, as per property:
color(blue)(a^2-b^2 = (a+b)(a-b)

So, ${x}^{2} - 25 = \left(x + 5\right) \left(x - 5\right)$

The expression now becomes
$= \frac{\left(- x + 5\right)}{\left(x + 5\right) \left(x - 5\right)}$

$= \frac{- \cancel{\left(x - 5\right)}}{\left(x + 5\right) \cancel{x - 5}}$
=color(blue)(-1/(x+5)