# How does this denominator cancel out to create the next step?

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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## 2 Answers

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

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I ended up doing something similar, except like $\frac{\Delta x(2x + \Delta x)}{\Delta x}= 2x + \Delta x$ –  Jason Feb 14 '11 at 13:54
@Jason: that works, too. –  Ross Millikan Feb 14 '11 at 14:09

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?

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