Problem 49 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The result of adding \(\frac{3}{2x+4}\) and \(\frac{2}{3x+6}\) is \(\frac{13}{6x+12}\).

Step 1: Identify the denominators

The denominators for the two fractions are \(2x+4\) and \(3x+6\).

Step 2: Finding the common denominator

We need a common denominator to add these two fractions. The lowest common denominator of \(2x+4\) and \(3x+6\) is \(6x+12\) which can be deduced as it is common multiple of both.

Step 3: Convert to common denominator

Convert each fraction to the equivalent fraction with this common denominator. This is done by multiplying the numerator and denominator of each fraction by the factor that the denominator needs to become the common denominator.\nThe first fraction becomes \(\frac{3}{2x+4} * \frac{3}{3} = \frac{9}{6x+12}\) and the second one becomes \(\frac{2}{3x+6} * \frac{2}{2} = \frac{4}{6x+12}\)

Step 4: Add the fractions

We can now add these fractions as they have the same denominator: \(\frac{9}{6x+12} + \frac{4}{6x+12} = \frac{9+4}{6x+12}\)

Step 5: Simplify the result

Simplify the resulting fraction by combining the numerators: \(\frac{13}{6x+12}\)