Help PreCalc Hw?

Question

use the link for pic could you please explain steps in detail and specify the answer thnx http://i128.photobucket.com/albums/p199/av611/r.jpg

Answer 1

Plug in the value (x+h) wherever you see the (x) in the original equation and then continue normally:
=[3(x+h)^4-5(x+h)^2+2(x+h)]-[3x^4-5x^2+2x]/x

=[(3x^4+12x^3h+18x^2h^2+12xh^3+3h^4)-(5x^2+10xh+5h^2)+(2x+2h)]-[3x^4-5x^2+2x]/x

Now, the 3x^4s cancel out, the 5x^2s cancel out, the 2x's cancel out, so all that's left is:

=[12x^3h+18x^2h^2+12xh^3+3h^4-10x-5h^2+2h]/x