Question
Reduce the given Rational expression to its lowest form
$
\frac{x^{3 a }-8}{x^{2 a }+2 x^{ a }+4}
$
$
\frac{x^{3 a }-8}{x^{2 a }+2 x^{ a }+4}
$
✓
Answer
$\begin{aligned} & x^{3 a}-8=\left(x^a\right)^3-2^3 \ldots\left(\text { using the formula } a^3-b^3=(a-b)\left(a^2+a b+b^2\right)\right. \\ & =\left(x^a-2\right)\left[\left(x^a\right)^2+x^a \times 2+2^2\right] \\ & =\left(x^a-2\right)\left(x^{2 a}+2 x^a+4\right) \\ & \frac{x^{3 a}-8}{x^{2 a}+2 x^a+4}=\frac{\left(x^a-2\right)\left(x^{2 a}+2 x^a+4\right)}{\left(x^{2 a}+2 x^a+4\right)} \\ & =x^a-2\end{aligned}$
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