I need help with solving a complex fraction

[Violagirl]

Simplify the following fraction:

4a/a+1/a

So far I've added a one under the a in the denominator and then muliplied a into the denominator and numerator, getting

4a/a^2/a+1/a. Next I added the denominator and got 4a/2a^2/a. Then I changed the denominator around to get: 4a x a/2a^2.

Lastly I I divided out the 4 and 2 and subtracted the variables to get an answer of 2/a. I'm not sure what I did wrong.

 

[Loren]

4a/a+1/a means \(\displaystyle \frac{4a}{a}+\frac{1}{a}\). If that is what you mean, then you need to recognize the fact that the two fractions have the same (common) denominator. To add two fractions with a common denominator, the sum of the numerators is the numerator of the sum and the common denominator is its denominator.

 

[Violagirl]

That's actually different from what I was trying to type. I'll try it again. Sorry about that!
Simplify the following complex fraction.


(4a)/(a+1/a)

 

[Deleted member 4993]

That's actually different from what I was trying to type. I'll try it again. Sorry about that!
Simplify the following complex fraction.


(4a)/(a+1/a)

Does your problem then look like:

\(\displaystyle \frac{4\cdot a}{a\, + \, \frac{1}{a}}\)

then

\(\displaystyle = \, \frac{4\cdot a}{\frac{(a^2 + 1)}{a}}\)

\(\displaystyle = \, 4\cdot a}\, \cdot \,\frac{a}{(a^2 + 1)}\)

\(\displaystyle = \, \frac{4\cdot a^2}{(a^2 + 1)}\)

 

[Violagirl]

Oh I get it! Yes, that's how the first part is orginally set up in my book. Thanks!