Question 818808
A way to check would be to multiply {{{3x^3-2x-5+((-8x-34)/(x^2-4))}}} by {{{(x^2-4)}}}:
{{{(3x^3-2x-5+((-8x-34)/(x^2-4)))(x^2-4)}}}
Using the Distributive Property:
{{{(3x^3)(x^2-4)+(-2x)(x^2-4)+(-5)(x^2-4)+((-8x-34)/(x^2-4))(x^2-4)}}}
{{{3x^5+(-12x^3)+(-2x^3)+8x+(-5x^2)+20+(-8x)+(-34)}}}
{{{3x^5+(-14x^4)+(-5x^2)+(-14)}}}
So, yes, you got it right.