Simplify 1/x+1 + 1/x-1

Correct Answer is : 2x/(x + 1)(x−1)

Correct Answer is : 2x/(x + 1)(x−1)

Test Index

JAMB Mathematics 2015 Paper

Question : 45

Total: 61

Simplify

\frac{1}{x+1} + \frac{1}{x-1}

Solution:

Concept:

Adding algebraic fractions requires a common denominator.

Explanation:

Consider

\frac{1}{x+1} + \frac{1}{x-1}

The least common denominator (LCD) is

(x+1)(x-1)

Rewrite each fraction with this common denominator.

\frac{1}{x+1} = \frac{1(x-1)}{(x+1)(x-1)} = \frac{x-1}{(x+1)(x-1)}

\frac{1}{x-1} = \frac{1(x+1)}{(x+1)(x-1)} = \frac{x+1}{(x+1)(x-1)}

Now add the numerators:

\frac{x-1}{(x+1)(x-1)} + \frac{x+1}{(x+1)(x-1)} = \frac{(x-1)+(x+1)}{(x+1)(x-1)}

Simplify the numerator:

x-1+x+1 = 2x

Thus, the sum equals

\frac{2x}{(x+1)(x-1)}

No further simplification is possible.

Answer:

Option B:

\frac{2x}{(x+1)(x-1)}

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