Question

Simplify:
$\left[\frac{x^3+y^3}{(x-y{)}^2+3xy}\right]+\left[\frac{(x+y{)}^2-3xy}{x^3-y^3}\right]\times \frac{xy}{x^2-y^2}$.

• A. $1$
• B. $2xy$
• C. $xy$
• D. None of these

Answer 1

The correct option is D None of these

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

$\frac{x^3+y^3}{(x-y{)}^2+3xy}=x+y$

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