Problem 38 - College Algebra Essentials

Question

Add or subtract as indicated. $$\frac{2 x+3}{3 x-6}-\frac{3-x}{3 x-6}$$

Step-by-Step Solution

Answer

The answer is \(\frac{3x}{3x - 6}\)

Step 1: Observation

Given two fractions \(\frac{2 x+3}{3 x-6}\) and \(\frac{3-x}{3 x-6}\) with the same denominator. We are required to subtract the second fraction from the first.

Step 2: Carry out the Subtraction

Since both fractions have the same denominator, their difference can be written with a common denominator. We obtain: \(\frac{2 x+3-(3-x)}{3 x-6}\)

Step 3: Simplify the Numerator

Distribute the negative sign in the numerator: \(\frac{2x + 3 - 3 + x}{3x - 6}\)

Step 4: Combine Like Terms

Combine like terms in the numerator, to simplify the expression. The result is: \(\frac{3x}{3x - 6}\)

Step 5: Simplify the Fraction

Unfortunately, the fraction \(\frac{3x}{3x - 6}\) cannot be simplified further.