Express 2/x+3 - 1/x-2 as a simple fraction

Correct Answer is : x−7x2+x−6x-7/x²+x-6x2+x−6x−7

Correct Answer is : x−7x2+x−6x-7/x²+x-6x2+x−6x−7

Test Index

WAEC Mathematics 2013 Paper

Question : 27

Total: 48

Express

\frac{2}{x+3} - \frac{1}{x-2}

as a simple fraction

Solution:

Concept:

Combine two algebraic fractions by taking the lowest common denominator

(x+3)(x-2)

Explanation:

Rewrite each fraction with the common denominator

(x+3)(x-2)

\frac{2}{x+3} - \frac{1}{x-2} = \frac{2(x-2) - 1(x+3)}{(x+3)(x-2)}

Expand the numerator:

2(x-2) - (x+3) = 2x - 4 - x - 3 = x - 7

Expand the denominator:

(x+3)(x-2) = x^2 - 2x + 3x - 6 = x^2 + x - 6

Therefore, the simplified fraction is

\frac{x-7}{x^2+x-6}

Answer:

\frac{x-7}{x^2+x-6}

(Option A).

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