if 0 < x < y and x/y=r which of the following must be equal to x+y/x
(A) 1 over (r + 1)
(B) r over (r + 1)
(C) (r +1) over (r minus 1)
(D) (r + 1) over r
(E) r plus 1
can you please explain how the answer is D.

First, please always use parentheses when you enter fractions. You did in the answer choices, but not the question itself. I have seen this question before so I know it should be (x + y)/x, but that’s not what you typed.

Anyhoo, manipulate the fraction:


Since you know that \dfrac{x}{y}=r, you know that \dfrac{y}{x}=\dfrac{1}{r}, so you can simplify the above:


If you combine that into one fraction by getting a common denominator, you land on choice D:


Don’t like all that algebra? This is also a great question to plug in on! 🙂

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