Question

What is the numerator of the simplified sum? X/x^2+3x+2 + 3/x+1

Answer 1

`4x + 6`

that's the numerator

Answer 2

`(2(2x+3))/((x+2)(x+1))= (4x+6)/((x+2)(x+1))`

And the numerator for the simplied sum is
`4x+6`

Explanation:

For this case we have the following expression :

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

And we can begin doing this:

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

Now we can distribute the terms on the numerator, and factorize the
`x^2 +3x+ +2 = (x+1)(x+2)` on the denominator and we got:

`(x^2 +x + 3x^2 +9x +6)/((x+2) (x+1)^2)`

`(4x^2 +10x +6)/((x+2) (x+1)^2)`

We can now factorize the nuemrator like this:

`4x^2 +10x + 6 = (2x+2) (2x+3)`

And if we replace this we got:

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

Now we can take common factor 2 on the numerator like this:

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

And we can cancel the x+1 on the numerator and denominator like this:

`(2(2x+3))/((x+2)(x+1))= (4x+6)/((x+2)(x+1))`

And the numerator for the simplied sum is
`4x+6`