Given the function g(x)=5−x^2, simplify g(x+h) − g(x)h, h≠0.

Question

my answer: (5-x^2)-(-x^2+5))/0

Answer 1

You have a typo, you wanted :
( g(x+h) − g(x) ) / h, h≠0

g(x) = 5 - x^2
g(x+h) = 5 - (x+h)^2 = 5 - (x^2 + 2hx + h^2)
= 5 - x^2 - 2hx - h^2

( g(x+h) − g(x) ) / h
=(5 - x^2 - 2hx - h^2 - (5 - x^2) )/h
= (5 - x^2 - 2hx - h^2 - 5 + x^2)/h
= (-2hx - h^2)/h
= -2x - h , h ≠ 0

You did not evaluate g(x+h) correctly