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Morgarella [4.7K]
3 years ago
10

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

Mathematics
1 answer:
stich3 [128]3 years ago
7 0

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}.

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