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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 result of adding these two fractions is 2.

Step by step solution

01

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.
02

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 \(\frac{6x+8}{3x+4}\) .
03

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.

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