Question

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

Answer 1

Given:

The expression is

`(2)/(a-2)-(8)/(a^2-4)`

To find:

The simplified form of the given expression.

Solution:

We have,

`(2)/(a-2)-(8)/(a^2-4)`

It can be written as

`=(2)/(a-2)-(8)/(a^2-2^2)`

`=(2)/(a-2)-(8)/((a-2)(a+2))`
`[\because a^2-b^2=(a-b)(a+b)]`

Taking LCM, we get

`=(2(a+2)-8)/((a-2)(a+2))`

`=(2a+4-8)/((a-2)(a+2))`

`=(2a-4)/((a-2)(a+2))`

`=(2(a-2))/((a-2)(a+2))`

Cancel out the common factors.

`=(2)/(a+2)`

Therefore, the simplified form of the given expression is
`(2)/(a+2)`.