Simplify 2/2+x + 2/2-x

Correct Answer is : 84−x28/4-x²4−x28

Correct Answer is : 84−x28/4-x²4−x28

Test Index

WAEC Mathematics 2010 Paper

Question : 20

Total: 49

Simplify

\frac{2}{2+x} + \frac{2}{2-x}

Solution:

Concept:

Addition of algebraic fractions requires a common denominator.

Explanation:

The denominators are

(2+x)

and

(2-x)

Their product

(2+x)(2-x) = 4 - x^{2}

is the common denominator.

Rewrite each fraction with this denominator:

\frac{2}{2+x} + \frac{2}{2-x} = \frac{2(2-x) + 2(2+x)}{(2+x)(2-x)}

Simplify the numerator:

2(2-x) = 4 - 2x

and

2(2+x) = 4 + 2x

So, numerator

= 4 - 2x + 4 + 2x = 8

Therefore, the expression becomes

\frac{8}{4 - x^{2}}

Answer:

\frac{8}{4-x^{2}}

which is Option B.

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