Question 1095036
<font color="black" face="times" size="3">First compute g(x+h):


{{{g(x) = x^2}}}


{{{g(x+h) = (x+h)^2}}} Replace every x with x+h


{{{g(x+h) = (x+h)(x+h)}}}


{{{g(x+h) = x(x+h)+h(x+h)}}}


{{{g(x+h) = x^2+xh+xh+h^2}}}


{{{g(x+h) = x^2+2xh+h^2}}}


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Now find the Difference Quotient:


{{{(g(x+h) - g(x))/h = (x^2+2xh+h^2 - x^2)/h}}}


{{{(g(x+h) - g(x))/h = (2xh+h^2)/h}}} Note how the x^2 terms subtract and cancel 


{{{(g(x+h) - g(x))/h = (h(2x+h))/h}}} Factor out the GCF h


{{{(g(x+h) - g(x))/h = (cross(h)(2x+h))/(cross(h))}}} Divide the h terms and cancel


{{{(g(x+h) - g(x))/h = 2x+h}}} Simplify


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So when everything is fully simplified, the final answer is {{{2x+h}}}</font>