Add or subtract, as indicated. (7x + 8)/(3x + 2) - (x + 4)/(3x + 2)

Verified step by step guidance

1. Identify that both rational expressions have the same denominator, which is \(3x + 2\).
2. Since the denominators are the same, you can combine the numerators directly by subtracting: \(\frac{7x + 8}{3x + 2} - \frac{x + 4}{3x + 2} = \frac{(7x + 8) - (x + 4)}{3x + 2}\).
3. Distribute the subtraction across the second numerator: \((7x + 8) - (x + 4) = 7x + 8 - x - 4\).
4. Combine like terms in the numerator: \(7x - x = 6x\) and \(8 - 4 = 4\), so the numerator becomes \(6x + 4\).
5. Write the simplified expression as \(\frac{6x + 4}{3x + 2}\), which is the result of the subtraction.

Key Concepts

Like Denominators in Rational Expressions

When adding or subtracting rational expressions with the same denominator, you combine only the numerators while keeping the denominator unchanged. This simplifies the process, similar to adding fractions with a common denominator.

Combining Like Terms in the Numerator

After combining the numerators, you simplify by combining like terms—terms that have the same variable raised to the same power. This step reduces the expression to its simplest form.

Simplifying Rational Expressions

Once the numerator is combined, check if the resulting expression can be factored or simplified further by canceling common factors with the denominator. This ensures the expression is in its simplest form.