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Chapter 0: Problem 34

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

Short Answer

Expert verified
The final simplified answer is 2.

Step by step solution

01

Identify the common denominator

Both given fractions, \(\frac{3x+2}{3x+4}\) and \(\frac{3x+6}{3x+4}\), share the same denominator, which is 3x + 4.
02

Add the fractions

When fractions have the same denominator, they can simply be added by adding the numerators. In this case, add \(3x + 2\) and \(3x + 6\) getting \(6x + 8\) as the new numerator. So, the result of the addition is \(\frac{6x+8}{3x+4}\).
03

Simplification

The result \(\frac{6x + 8}{3x + 4}\) can be simplified further by factoring. The numerator can be factored as \(2(3x + 4)\) and the denominator is \(3x + 4\), which simplifies to 2, as the term \(3x + 4\) cancels out from both the numerator and the denominator.

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