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WAEC Mathematics 2021 Paper

Question : 23

Total: 49

\frac{2}{x-3}

\frac{3}{x-2}

\frac{p}{(x-3)(x-2)}

, find p.

Solution:

Concept:

Combine two algebraic fractions by taking their common denominator.

Explanation:

The common denominator of

\frac{2}{x-3}

and

\frac{3}{x-2}

(x-3)(x-2)

Rewrite each fraction with this denominator:

\frac{2}{x-3} = \frac{2(x-2)}{(x-3)(x-2)}

\frac{3}{x-2} = \frac{3(x-3)}{(x-3)(x-2)}

Subtract the second fraction from the first:

\frac{2(x-2)-3(x-3)}{(x-3)(x-2)}

Simplify the numerator:

2x-4-3x+9 = 5-x

Therefore:

\frac{2}{x-3} - \frac{3}{x-2} = \frac{5-x}{(x-3)(x-2)}

Comparing with

\frac{p}{(x-3)(x-2)}

, we get

p = 5-x

Answer:

p = 5-x

Option A.

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