Simplify the difference Quotient?

Question

#(f(2+h) -f(2))/h# if h is not 0

#f(x) = x^2-6x#

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Answer 1 · 2018-02-18T18:25:10

#h-4#

#((2+h)^2-6(2+h)-(-8))/h#

#(4+4h+h^2-12-6h+8)/h#

#(h^2-2h)/h#

#h-#2

Answer 2 · 2018-02-18T18:25:35

#h-2#

#f(x)=x^2-6x#

#[f(x+h)-f(x)]/h#
#=[(x+h)^2-6(x+h)-(x^2-6x)]/h#
#=(x^2+2xh+h^2-6x-6h-x^2+6x)/h#
#=(2xh+h^2-6h)/h#
#=[h(2x+h-6)]/h#
#=2x+h-6#

#[f(2+h)-f(2)]/h#
#=2*2+h-6#
#=h-2#