Question

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

Explanation:

Step1: Factor the denominator

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

Step2: Find a common - denominator

The common denominator of the two fractions is $(x + 1)(x + 2)$. Rewrite $\frac{3}{x + 1}$ as $\frac{3(x + 2)}{(x + 1)(x + 2)}=\frac{3x+6}{(x + 1)(x + 2)}$.

Step3: Add the fractions

$\frac{x}{(x + 1)(x + 2)}+\frac{3x + 6}{(x + 1)(x + 2)}=\frac{x+(3x + 6)}{(x + 1)(x + 2)}=\frac{4x+6}{(x + 1)(x + 2)}$.

Answer:

$4x + 6$