Question

How do you add or subtract `(x^2+3x+2)/(x^2-16)+(3x+6)/(x^2-16)`?

Answer 1

Since both fractions have the same denominator, you can simply add up (or substract) the numerators and keep the denominator unchanged :

`(x^2 + 3x +2)/(x^2-16) + (3x+6)/(x^2-16) = ((x^2 + 3x +2)+(3x+6))/(x^2-16)`

`= (x^2 + 6x + 8)/(x^2 -16)`.

Then, you can factorize it :

`(x^2 + 6x + 8)/(x^2 -16) = ((x+2)(x+4))/((x+4)(x-4)) = (x+2)/(x-4)`.

In the case of a substraction :

`(x^2 + 3x +2)/(x^2-16) - (3x+6)/(x^2-16) = ((x^2 + 3x +2)-(3x+6))/(x^2-16)`

`= (x^2 - 4)/(x^2 -16) = ((x+2)(x-2))/((x+4)(x-4))`.