Algebra

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

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

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  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

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