Question

Help! Pls I cant solve it help me with explanation also pls.

Answer 1

Given:

The expression is

$\dfrac{2}{a-2}-\dfrac{8}{a^2-4}$

To find:

The simplified form of the given expression.

Solution:

We have,

$\dfrac{2}{a-2}-\dfrac{8}{a^2-4}$

It can be written as

$=\dfrac{2}{a-2}-\dfrac{8}{a^2-2^2}$

$=\dfrac{2}{a-2}-\dfrac{8}{(a-2)(a+2)}$            $[\because a^2-b^2=(a-b)(a+b)]$

Taking LCM, we get

$=\dfrac{2(a+2)-8}{(a-2)(a+2)}$

$=\dfrac{2a+4-8}{(a-2)(a+2)}$

$=\dfrac{2a-4}{(a-2)(a+2)}$

$=\dfrac{2(a-2)}{(a-2)(a+2)}$

Cancel out the common factors.

$=\dfrac{2}{a+2}$

Therefore, the simplified form of the given expression is $\dfrac{2}{a+2}$.