Question

Adding/Subtracting Rational Expressions ​

Answer 1

9514 1404 393

Answer:

(4x^2 +21x +18)/(3x^2 +34x -24)

Explanation:

I find it helpful to keep in mind the form ...

a/b + c/d = (ad +bc)/(bd)

When we apply that to this case, we get ...

`(x+3)/(x+12)+(x+2)/(3x-2)=((x+3)(3x-2)+(x+12)(x+2))/((x+12)(3x-2))\\\\=((3x^2+7x-6)+(x^2+14x+24))/((x+12)(3x-2))=\boxed{(4x^2+21x+18)/(3x^2+34x-24)}`