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I was following an example in my text, and there was one step I got stuck on.

Given $\frac{2x(\Delta x) + (\Delta x)^{2}}{\Delta x}$, how does the denominator cancel out to produce $2c+\Delta x$?

My thinking is that the formula expands to $\frac{2x(\Delta x) + (\Delta x * \Delta x)}{\Delta x}$, but how does the denominator cancel out on both sides of the + sign if the numerator is one formula?

*Edited the formula to be multiplication instead of addition

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$\frac{2x(\Delta x) + (\Delta x)^{2}}{\Delta x}=\frac{2x(\Delta x)}{\Delta x} + \frac{(\Delta x)^{2}}{\Delta x}= 2x +\Delta x$.

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    @Jason: that works, too.2011-02-14
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Jason, you have mistakenly rewritten $(\Delta x)^2$ as $\Delta x+\Delta x$, rather than as $\Delta x \cdot \Delta x$. Is this the problem?