Dividing and adding fractions with 2 variables

[daffy88]

I cannot guarantee that this is "intermediate" algebra, but I think of myself as more or less knowledgable of basic algebra, and I cannot figure this out for the life of me:

2 / 2/x + 2/y

When I do the problem, I come out with xy/2, which I know is incorrect because, first of all, that is not an answer choice, and second of all, I peeked at the answer and it is xy/x+y. I do not understand how to get to the correct answer. My work to get xy/2:

2 / 2/x + 2/y =
2 * x/2 + y/2 =
2/1(x/2 + y/2) =
2x/2 + 2y/2 =
2x + 2y/4 =
xy/2

Any help available to explain what I am doing wrong or not doing? Thanks!

 

[Loren]

I cannot guarantee that this is "intermediate" algebra, but I think of myself as more or less knowledgable of basic algebra, and I cannot figure this out for the life of me:

2 / 2/x + 2/y <<< Not clear as to what this means. You need to use parenthesis to clarify.

When I do the problem, I come out with xy/2, which I know is incorrect because, first of all, that is not an answer choice, and second of all, I peeked at the answer and it is xy/x+y. I do not understand how to get to the correct answer. My work to get xy/2:

2 / 2/x + 2/y = ??? \(\displaystyle \frac{2}{\frac{2}{x}}+\frac{2}{y}\)
2 * x/2 + y/2 = ??? \(\displaystyle 2\cdot \frac{x}{2}+\frac{y}{2}\)
2/1(x/2 + y/2) =
2x/2 + 2y/2 =
2x + 2y/4 =
xy/2

\(\displaystyle 2\cdot \frac{x}{2}+\frac{y}{2}=\)

\(\displaystyle x+\frac{2}{y}=\)

\(\displaystyle \frac{xy}{y}+\frac{2}{y}\)

\(\displaystyle \frac{xy+2}{y}\)

Any help available to explain what I am doing wrong or not doing? Thanks!