Question

The simplified form of $\frac{x^2-9y^2}{x^3-27y^3}$ is _______.

• A. $\frac{x+3y}{x^2+3xy+9y^2}$
• B. $\frac{x^2+3xy+9y^2}{x+3y}$
• C. $\frac{x^2+6xy+9y^2}{x+3y}$
• D. $x+3y$

Answer 1

The correct option is A $\frac{x+3y}{x^2+3xy+9y^2}$

Given,
$\frac{x^2-9y^2}{x^3-27y^3}$
$\frac{x^2-9y^2}{x^3-27y^3}$ = $\frac{x^2-(3y{)}^2}{x^3-(3y{)}^3}$

= $\frac{(x+3y)(x-3y)}{(x-3y)(x^2+3xy+9y^2)}$ $[\because a^2-b^2=(a+b\left)\right(a-b)and{a}^3-b^3=(a-b\left)\right(a^2+ab+b^2]$

= $\frac{x+3y}{x^2+3xy+9y^2}$