Question

simplify the rational expression $\frac{3x^{2}}{2x^{3}-6x}$
$\frac{3x}{2x^{2}-6}$
$\frac{3}{2x - 6}$
1
-1

Explanation:

Step1: Factor the denominator

Factor out \(2x\) from \(2x^{3}-6x\), we get \(2x(x^{2} - 3)\). So the original expression \(\frac{3x^{2}}{2x^{3}-6x}=\frac{3x^{2}}{2x(x^{2}-3)}\).

Step2: Simplify the fraction

Cancel out the common factor \(x\) (assuming \(x
eq0\)) between the numerator and the denominator. \(\frac{3x^{2}}{2x(x^{2}-3)}=\frac{3x}{2(x^{2}-3)}=\frac{3x}{2x^{2}-6}\)

Answer:

A. \(\frac{3x}{2x^{2}-6}\)