Simplify: x² - y²/(x+y)² ÷ (x-y)²/3x+3y

Correct Answer is : 3x−y3/x-yx−y3

Correct Answer is : 3x−y3/x-yx−y3

Test Index

WAEC Mathematics 2013 Paper

Question : 9

Total: 48

Simplify:

\frac{x^2 - y^2}{(x+y)^2} \div \frac{(x-y)^2}{3x+3y}

Solution:

Concept:

Use factorization and division of algebraic fractions.

Explanation:

Rewrite the division as multiplication by the reciprocal.

\frac{x^2 - y^2}{(x+y)^2} \div \frac{(x-y)^2}{3x+3y} = \frac{x^2 - y^2}{(x+y)^2} \times \frac{3x+3y}{(x-y)^2}

Factorise each expression.

x^2 - y^2 = (x+y)(x-y)

3x+3y = 3(x+y)

So the expression becomes:

\frac{(x+y)(x-y)}{(x+y)^2} \times \frac{3(x+y)}{(x-y)^2}

Cancel common factors of

(x+y)

and

(x-y)

This gives

\frac{3}{x-y}

Answer:

\frac{3}{x-y}

Correct option: C.

Go to Question:

Prev Question

Next Question