Question 1113382
You most certainly wanted to ask for {{{  (f(x+h)-f(x))/h  }}} and not {{{   f(x+h)-f(x)/h  }}}
(Use paren's)

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{{{  (f(x+h)-f(x))/h  =  ( ((x+h)^2 + 3)  - (x^2 + 3)) / h  }}}
= {{{ ( ((x^2 + 2hx + h^2) + 3) - (x^2 + 3)) / h }}}
= {{{ ( x^2 + 2hx + h^2 + 3  - x^2 - 3) / h }}}
= {{{ ( cross( x^2) + 2hx + h^2 + cross(3)  - cross( x^2) - cross(3)) / h }}}  
= {{{  (   2hx + h^2 ) / h }}}
= {{{  highlight ( 2x + h) }}}

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Just some seeds for your mathematical future:
In Calculus I, you will learn about the derivative (= rate of change) of a function.   This problem is leading up to the basis for the derivative, where one finds the limit of (f(x+h)-f(x))/h  as h—>0  (here it would be 2x because  h vanishes as h—>0).