Question

Rational expression $\frac{y^3-8}{y^2-4}$ written in its lowest form is .

• A. $\frac{y^2+2y+4}{y+2}$
• B. $\frac{y^2+2y+4}{y-2}$
• C. $\frac{y^2+y+4}{y+2}$
• D. $\frac{y^2+y+4}{y-2}$

Answer 1

The correct option is A $\frac{y^2+2y+4}{y+2}$

Given expression: $\frac{y^3-8}{y^2-4}$

Here, $p\left(x\right)=y^3-8=y^3-2^3$
= $(y-2)(y^2+2y+4)$
$q\left(x\right)=y^2-4=y^2-2^2$
= $(y+2)(y-2)$

Now $\frac{p\left(x\right)}{q\left(x\right)}=\frac{(y-2)(y^2+2y+4)}{(y+2)(y-2)}$

Cancelling $(y-2)$ from numerator and denominator,

$\frac{p\left(x\right)}{q\left(x\right)}=\frac{(y^2+2y+4)}{(y+2)}$