Problem 34 - College Algebra Essentials

Question

Add or subtract as indicated. $$\frac{3 x+2}{3 x+4}+\frac{3 x+6}{3 x+4}$$

Step-by-Step Solution

Answer

The sum of the fractions \( \frac{3x+2}{3x+4} \) and \( \frac{3x+6}{3x+4} \) is \( \frac{6x+8}{3x+4} \)

Step 1: Identify the Terms

The given expression is composed of two fractions: \( \frac{3x+2}{3x+4} \) and \( \frac{3x+6}{3x+4} \). Both fractions have the same denominator \(3x+4\), which facilitates the process since the denominators do not need to be made equal.

Step 2: Add the Fractions

Since both fractions have the same denominator, they can be added directly. The denominator will remain as \(3x+4\) while the numerators will be added, thus resulting in: \( \frac{(3x+2)+(3x+6)}{3x+4} \)

Step 3: Simplify the Numerator

Combining the similar terms in the numerator results in \( \frac{6x+8}{3x+4} \)