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

4x + 6

Explanation:

Given

`(x)/(x^2+3x+2)` +
`(3)/(x+1)`

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

Factor the denominator of the first fraction

`(x)/((x+1)(x+2))` +
`(3)/(x+1)`

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

=
`(x)/((x+1)(x+2))` +
`(3(x+2))/((x+1)(x+2))` ← fractions now have a common denominator

Add the numerators leaving the denominators

=
`(x+3(x+2))/((x+1)(x+2))`

=
`(x+3x+6)/((x+1)(x+2))`

=
`(4x+6)/((x+1)(x+2))` ← simplified sum with numerator 4x + 6