Question

simplify each expression.

1. \\(\frac{6x + 24}{x^2 + 7x + 12}\\)

Explanation:

Step1: Factor numerator and denominator

Factor out 6 from the numerator: \(6x + 24 = 6(x + 4)\)
Factor the quadratic in the denominator: \(x^2 + 7x + 12=(x + 3)(x + 4)\)
So the expression becomes \(\frac{6(x + 4)}{(x + 3)(x + 4)}\)

Step2: Cancel common factors

Cancel the common factor \((x + 4)\) (assuming \(x
eq - 4\)): \(\frac{6\cancel{(x + 4)}}{(x + 3)\cancel{(x + 4)}}=\frac{6}{x + 3}\)

Answer:

\(\frac{6}{x + 3}\) (for \(x
eq - 3,-4\))