Question

What is the numerator of the simplified sum? StartFraction x Over x squared + 3 x + 2 EndFraction + StartFraction 3 Over x + 1 EndFraction

Answer 1

Answer:

4x + 6

Step-by-step explanation:

Given

$\frac{x}{x^2+3x+2}$ + $\frac{3}{x+1}$

Before we can add the fractions we require them to have a common denominator.

Factor the denominator of the first fraction

$\frac{x}{(x+1)(x+2)}$ + $\frac{3}{x+1}$

Multiply the numerator / denominator of the second fraction by (x + 2)

= $\frac{x}{(x+1)(x+2)}$ + $\frac{3(x+2)}{(x+1)(x+2)}$ ← fractions now have a common denominator

Add the numerators leaving the denominators

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

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

= $\frac{4x+6}{(x+1)(x+2)}$ ← simplified sum with numerator 4x + 6