Question

If $x:y=7:3,$ then the value of $\frac{xy+y^2}{x^2-y^2}$ is:

• A. $\frac{3}{4}$
• B. $\frac{4}{3}$
• C. $\frac{3}{7}$
• D. $\frac{7}{3}$

Answer 1

Answer: (A)

$\frac{3}{4}$

Let $x=7a;y=3a$
So, $\frac{xy+y^2}{x^2-y^2}=\frac{\left(7a\right)\left(3a\right)+(3a{)}^2}{(7a{)}^2-(3a{)}^2}$

$=\frac{21a^2+9a^2}{49a^2-9a^2}$

$=\frac{30a^2}{40a^2}$ $=\frac{3}{4}$

Hence, option A.