Question

Simplify the expression. $$\frac{x}{3 x^{2}+2 x-8} \cdot(3 x-4)$$

Short answer

The simplified expression is \(-2\).

Step-by-step solution

Distribute the term

The term \(3x - 4\) can be distributed over the fraction \(\frac{x}{3x^2 + 2x - 8}\). This gives us the expression \(\frac{x \cdot (3x - 4)}{3x^2 + 2x - 8}\).

Simplify the expression

The expression can now be simplified by multiplying out the terms in the numerator. This results in the expression \(\frac{3x^2 - 4x}{3x^2 + 2x - 8}\).

Cancel out common factors

It is now possible to cancel out the '3x^2' term from both the numerator and the denominator. After doing so, the left expression is \(\frac{-4x}{2x - 8}\). After reducing the terms, the resulting expression is \(-2\).