Simplify; \;a/b - \;b/a - \;c/b

Correct Answer is : a2 − b2 − acab\;{a²\; - \; b²\; - \; a c}{a b}aba2−b2−ac

\;a b\; - \; b c\; - \; a c/a b

\;{a²\; - \; b²\; + \; a c}{a b}

\;{a²\; - \; b²\; - \; a c}{a b}

Correct Answer is : a2 − b2 − acab\;{a²\; - \; b²\; - \; a c}{a b}aba2−b2−ac

Test Index

WAEC Mathematics 2020 Paper

Question : 22

Total: 48

Simplify;

\;\frac{a}{b} - \;\frac{b}{a} - \;\frac{c}{b}

Solution:

Concept:

Combine the algebraic fractions by rewriting each term with a common denominator.

Explanation:

The given expression is

\frac{a}{b} - \frac{b}{a} - \frac{c}{b}

The common denominator for

b

a

, and

b

ab

Rewrite each fraction with denominator

ab

\frac{a}{b} = \frac{a \times a}{a \times b} = \frac{a^2}{ab}

\frac{b}{a} = \frac{b \times b}{a \times b} = \frac{b^2}{ab}

\frac{c}{b} = \frac{c \times a}{b \times a} = \frac{ac}{ab}

Now combine the numerators:

\frac{a^2}{ab} - \frac{b^2}{ab} - \frac{ac}{ab} = \frac{a^2 - b^2 - ac}{ab}

This matches option D.

Answer:

\frac{a^{2} - b^{2} - ac}{ab}

Option D.

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