Question

find the sum of the terms.
\\(\frac{x}{x^2 + 3x + 2} + \frac{3}{x + 1}\\)
the numerator of the simplified sum is
options: (x + 3), (3x + 6), (4x + 6), (4x + 2)

Explanation:

Step1: Factor the denominator

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

Step2: Find a common denominator

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

Step3: Add the fractions

Add the numerators: \(\frac{x + 3(x + 2)}{(x + 1)(x + 2)}\). Expand the numerator: \(x + 3x + 6 = 4x + 6\).

Answer:

4x + 6