Question

$\frac{x^{4a}+2x^{2a}-48}{x^{4a}-64}$

Explanation:

Step1: Let \(y = x^{2a}\)

The expression becomes \(\frac{y^{2}+2y - 48}{y^{2}-64}\)

Step2: Factor the numerator and denominator

Factor \(y^{2}+2y - 48=(y + 8)(y - 6)\) and \(y^{2}-64=(y + 8)(y - 8)\)
So the expression is \(\frac{(y + 8)(y - 6)}{(y + 8)(y - 8)}\)

Step3: Cancel out the common factor

Cancel out \(y + 8\) (assuming \(y
eq - 8\), i.e., \(x^{2a}
eq - 8\)). We get \(\frac{y - 6}{y - 8}\)

Step4: Substitute back \(y = x^{2a}\)

The simplified expression is \(\frac{x^{2a}-6}{x^{2a}-8}\)

Answer:

\(\frac{x^{2a}-6}{x^{2a}-8}\)