Question

Simplify: $\frac{(x+y{)}^2-(x-y{)}^2}{x^{2}y-x{y}^2}$

• A. $\frac{1}{xy}$
• B. $\frac{1}{x-y}$
• C. $\frac{4}{x-y}$
• D. $\frac{2}{x-y}$

Answer 1

Answer: (C)

$\frac{4}{x-y}$

using $a^2-b^2=(a+b)(a-b)$

$(x+y{)}^2-(x-y{)}^2=4xy$

$x^{2}y-x{y}^2=xy(x-y)$

given expression $=\frac{(x+y{)}^2-(x-y{)}^2}{x^y-x{y}^2}=\frac{4xy}{xy(x-y)}=\frac{4}{x-y}$