Problem 67 - Introductory Algebra for College Students

Question

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{4-6 x}{3 x^{2}-2 x}$$

Step-by-Step Solution

Answer

\(\frac{4-6x}{3x^{2}-2x}\) simplified is \(\frac{4-6x}{x(3x-2)}\)

Step 1: Factor out common factors

Begin the simplification process by factoring out any common factors in both the numerator and the denominator. In this case, there are no common factors in the numerator but in the denominator, `x` can be factored out. Factoring gives: \(\frac{4-6x}{x(3x-2)}\)

Step 2: Check for common factors to cancel out

A rational expression is simplified when no common factors are left in the numerator and the denominator. Examine the numerator and the denominator of the expression obtained in step 1. If there are common factors, they are cancelled. In this case, there are no common factors in the numerator and the denominator. Therefore, this rational expression cannot be simplified further.