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WAEC Further Mathematics 2017 Paper

Question : 8

Total: 40

Given that

\frac{6x+m}{2x^{2}+7x-15} \equiv \frac{4}{x+5} - \frac{2}{2x-3}

, find the value of m.

Solution:

Concept:

Comparing numerators after combining the right-hand side into a single fraction.

Explanation:

The denominator on both sides is the same:

(x+5)(2x-3) = 2x^{2}+7x-15

Combine the right side using this common denominator:

\frac{4}{x+5} - \frac{2}{2x-3} = \frac{4(2x-3) - 2(x+5)}{(x+5)(2x-3)}

Simplify the numerator:

4(2x-3) - 2(x+5) = 8x - 12 - 2x - 10

= 6x - 22

Thus:

\frac{6x - 22}{2x^{2}+7x-15} \equiv \frac{6x+m}{2x^{2}+7x-15}

Comparing numerators gives:

6x + m = 6x - 22

m = -22

Answer:

m = -22

Option D.

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