Originally Posted by

**demode** I want to simplify

$\displaystyle (\frac{2u}{v}+\frac{2u+v}{v})$

If we add the two fractions we get $\displaystyle \frac{4u+v}{v}$, then we can just cancel out the v in the denominator by the v term on top to get $\displaystyle 4u$.

But apparently this is incorrect, since the correct answer has to be $\displaystyle \frac{4u}{v}+1$.

It seems that we must separate the fractions first $\displaystyle \frac{4u}{v} + \frac{v}{v} = \frac{4u}{v}+1$. But I do not understand why we couldn't just cancel the terms out, like we do in some other occasions! Can anyone explain?