Question

The rational expression:

$\frac{(x^2-xy-12y^2)(x^2+xy-12y^2)}{(x^2-16y^2)(x^2-9y^2)}$ when simplified equals

• A. 1
• B. xy
• C. (x + y)
• D. (x - y)

Answer 1

The correct option is A 1

$\frac{(x^2-xy-12y^2)(x^2+xy-12y^2)}{(x^2-16y^2)(x^2-9y^2)}$
$\Rightarrow \frac{(x^2-4xy+3xy-12y^2)(x^2+4xy-3xy-12y^2)}{({\left(x\right)}^2-{\left(4y\right)}^2)({\left(x\right)}^2-{\left(3y\right)}^2)}$
$\Rightarrow \frac{(x(x-4y)+3y(x-4y))(x(x+4y)-3y(x+4y))}{(x+4y)(x-4y)(x+3y)(x-3y)}$
$\Rightarrow \frac{(x+3y)(x-4y)(x-3y)(x+4y)}{(x+4y)(x-4y)(x+3y)(x-3y)}$
$\Rightarrow 1$