Question

simplify the expression completely if possible.
$\frac{4x}{12x^{2}-96x}$

Explanation:

Step1: Factor out the GCF in the denominator

First, find the greatest - common factor (GCF) of \(12x^{2}\) and \(96x\). The GCF of 12 and 96 is 12, and the GCF of \(x^{2}\) and \(x\) is \(x\). So, \(12x^{2}-96x = 12x(x - 8)\).
The expression becomes \(\frac{4x}{12x(x - 8)}\).

Step2: Simplify the fraction

Cancel out the common factors. The common factors of the numerator and the denominator are \(4x\).
\(\frac{4x}{12x(x - 8)}=\frac{4x}{4x\times3(x - 8)}=\frac{1}{3(x - 8)}\), where \(x
eq0\) (because when \(x = 0\), the original expression \(\frac{4x}{12x^{2}-96x}\) is undefined).

Answer:

\(\frac{1}{3(x - 8)},x
eq0\)