Question

subtract.
\\(\dfrac{3}{x^2 + 5x + 4} - \dfrac{2}{x + 4}\\)
simplify your answer as much as possible.

Explanation:

Step1: Factor the denominator

Factor \(x^2 + 5x + 4\) as \((x + 1)(x + 4)\). So the first fraction becomes \(\frac{3}{(x + 1)(x + 4)}\).

Step2: Find a common denominator

The common denominator of \(\frac{3}{(x + 1)(x + 4)}\) and \(\frac{2}{x + 4}\) is \((x + 1)(x + 4)\). Rewrite the second fraction with the common denominator: \(\frac{2(x + 1)}{(x + 1)(x + 4)}\).

Step3: Subtract the fractions

Subtract the numerators: \(3 - 2(x + 1)\). Expand and simplify the numerator: \(3 - 2x - 2 = 1 - 2x\). So the result is \(\frac{1 - 2x}{(x + 1)(x + 4)}\) or \(\frac{-2x + 1}{(x + 1)(x + 4)}\).

Answer:

\(\frac{-2x + 1}{(x + 1)(x + 4)}\) (or \(\frac{1 - 2x}{(x + 1)(x + 4)}\))