Problem 34 - College Algebra

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 result of adding these two fractions is 2.

Step 1: Identify the Common Denominator

The fractions are \(\frac{3x+2}{3x+4}\) and \(\frac{3x+6}{3x+4}\). In this case, the denominator \(3x+4\) is common to both fractions.

Step 2: Add the Numerators

Because the denominators of the fractions are common, the numerators can be added directly. Do \(3x+2 + (3x+6) = 6x+8\). So, the sum of the given fractions is \(\frac{6x+8}{3x+4}\) .

Step 3: Simplify the Result

The fraction \(\frac{6x+8}{3x+4}\) can be simplified by factoring out a 2 from the numerator. After simplification, we get \(2\left(\frac{3x+4}{3x+4}\right)\). Since \(3x+4\) is the same in the numerator and denominator, it will be canceled out and the final answer will be 2.