Problem 74 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

The simplified form of the given expression is \( \frac{x}{3} \)

Step 1: Factor out common terms

Start by factoring out any common terms from the numerator and the denominator: In the numerator, we can factor out \(x\), obtaining \(x(y-2)\). In the denominator, we can factor out \(3\), giving us \(3(y-2)\). So the expression becomes \(\frac{x(y-2)}{3(y-2)}\).

Step 2: Cancel common factors

Next, any common factors in the numerator and denominator should be cancelled out. Here, the term \((y-2)\) appears in both the numerator and denominator. So, it can be cancelled out, leaving us with \(\frac{x}{3}\).

Step 3: Double-check the simplified expression

Lastly, check the simplified expression. Ensure it can't be simplified any further. In this case, \(\frac{x}{3}\) is the simplest form of the rational expression. That's it, the problem is solved.