1. Complex fraction help

If 0<x<y and x/y=r, which of the following must be equal to x+y/x?

A
B
C
D
E

I don't understand how they did this.
I'm thinking it's because since x/y=r, if we moved the y over to the right, it'd be x=ry. So, in assuming that somehow y=1, then r multiplied by 1 would be r, thus x=r. And if x=r, then r would replace x in the fraction and 1 would replace y. But that doesn't make sense because why would y = 1? help. :P

2. You need to be more careful with parentheses. You have technically written x+(y/x), but I think you meant (x+y)/x. They are vastly different!

Try breaking the fraction apart and see where that leads.

3. Assuming that you mean $\frac{x + y}{x}$:

\begin{aligned}
\frac{x + y}{x} &= \frac{x}{x} + \frac{y}{x} \\
&= 1 + \frac{1}{r} \\
&= \frac{r}{r} + \frac{1}{r} \\
&= \frac{r + 1}{r}
\end{aligned}

4. Originally Posted by eumyang
Assuming that you mean $\frac{x + y}{x}$:

\begin{aligned}
\frac{x + y}{x} &= \frac{x}{x} + \frac{y}{x} \\
&= 1 + \frac{1}{r} \\
&= \frac{r}{r} + \frac{1}{r} \\
&= \frac{r + 1}{r}
\end{aligned}
Thank you! Also, I'll try to be more careful with my parenthesis Ackbeet. This isn't the first time you've told me iirc. :P