I need help with this math problem! A best answer will be chosen. Thanks!?

Question

Simplify the Fractional Expression:
(1-(x+h)/(2+(x+h))-((1-x)
/(2+x))/h (the whole thing is divided by h)

Answer 1

So for the function f(x) = (1 - x)/(2 + x), you are asked to find
(f(x+h) - f(x))/h, and then find the limit as h -> 0, is that it?

(f(x+h) - f(x))/h = {[1 - (x + h)]/[2 + (x + h)] - (1 - x) /(2 + x)}/h =
[(1-x-h)/(2+x+h) - (1-x)/(2+h)]/h =
[(1-x-h)(2+x) - (1-x)(2+x+h)]/h(2+x+h)(2+x) =
[2-2x-2h+x-x^2-xh-(2+x+h-2x-x^2-xh)/x(2+x+h)(2+x)=
-3h/h(2+x+h)(2+x) = -3/(2+x+h)(2+x).

Now as h -> 0, the above expression has limit -3/(2+x)^2.