1. ## Fraction Simplification

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?

2. 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?
Try writing out what you are saying with numbers instead of variables

for example

$\displaystyle \frac{3}{2}=\frac{1+2}{2}\not= \frac{1+\not{2}}{\not{2}}=1$

Remember that fraction bar represents division the opposite of division is multipication so we can only reduce factors (things that are multiplied togther ) accross a fraction bar.

i.e

$\displaystyle \frac{15}{3}=\frac{5\cdot 3}{3}=\frac{5\cdot \not{3}}{\not{3}}=5$

I hope this clears it up.

3. 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?
Dear demode,

Because you have to divide the whole numerator, (4u+v) by v. It is not just v in the numerator that you divide.