How can you evaluate $\frac{x}{x^{2} - 36} - \frac{6}{x^{2} - 36}$ $(x)/(x^2-36) - (6)/(x^2-36)$ ?

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Answer 1 · 2015-07-22T15:58:47

$= \frac{1}{x + 6}$ $=color(blue)(1/(x+6)$

$\frac{x}{x^{2} - 36} - \frac{6}{x^{2} - 36}$ $x/(x^2-36) - 6/(x^2-36)$

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

$= \frac{x - 6}{x^{2} - 36}$ $=(x-6)/(x^2-36)$

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

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

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)xx2−36−6x2−36(x)/(x^2-36) - (6)/(x^2-36)?