Add or subtract as indicated. (3x+2)/(3x+4) + (3x+6)/(3x+4)

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Identify that both rational expressions have the same denominator, which is \(3x+4\).

Since the denominators are the same, you can combine the numerators directly by adding them: \((3x+2) + (3x+6)\).

Add the numerators by combining like terms: \(3x + 3x = 6x\) and \(2 + 6 = 8\), so the numerator becomes \(6x + 8\).

Write the combined expression as a single fraction: \(\frac{6x + 8}{3x + 4}\).

Check if the numerator and denominator can be factored to simplify the expression further.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Adding and Subtracting Rational Expressions

To add or subtract rational expressions, they must have a common denominator. Once the denominators are the same, combine the numerators by addition or subtraction while keeping the denominator unchanged.

Simplifying Algebraic Expressions

After combining numerators, simplify the resulting expression by combining like terms and factoring if possible. This helps to write the expression in its simplest form for easier interpretation.

Common Denominator Identification

A common denominator is a shared multiple of the denominators of the rational expressions involved. In this problem, both denominators are identical, so the common denominator is simply that expression, allowing direct addition of numerators.

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