How can you evaluate $(x)/(x^2-36) - (6)/(x^2-36)$ ?

Question

1872 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-22T15:58:47

$=color(blue)(1/(x+6)$

$x/(x^2-36) - 6/(x^2-36)$

The denominators of both terms being common we can simply add the numerators:

$=(x-6)/(x^2-36)$

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

Expressing the denominator in the same manner:
$color(blue)((x^2-36) = (x+6)(x-6)$

The expression becomes:

$=cancel(x-6)/(color(blue)( (x+6)cancel(x-6))$

$=color(blue)(1/(x+6)$

How can you evaluate (x)/(x^2-36) - (6)/(x^2-36)(x)/(x^2-36) - (6)/(x^2-36)?