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If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =

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Bunuel
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If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) = [#permalink] If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =   01 Jun 2017, 12:04
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If \(\frac{x + y}{x − y} = \frac{1}{2}\), then \(\frac{xy + x^2}{xy − x^2}=\)


(A) –4.2

(B) –1/2

(C) 1.1

(D) 3

(E) 5.3

Source: Nova GMAT
Difficulty Level: 500
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B
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Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) = [#permalink] If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =   29 Jan 2021, 09:04
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Bunuel wrote:
If \(\frac{x + y}{x − y} = \frac{1}{2}\), then \(\frac{xy + x^2}{xy − x^2}=\)


(A) –4.2

(B) –1/2

(C) 1.1

(D) 3

(E) 5.3


Given: \(\frac{xy + x^2}{xy − x^2}\)

Factor numerator and denominator to get: \(\frac{x(y + x)}{x(y − x)}\)

Rewrite as follows: \((\frac{x}{x})(\frac{(y + x)}{(y − x)})\)

Simplify to get: \(\frac{(x + y)}{(y − x)}\)

Notice that this fraction ALMOST matches the given information \(\frac{x + y}{x − y} = \frac{1}{2}\).
No problem...
\(\frac{(x + y)}{(y − x)}=\frac{(x + y)}{-1(-y + x)}=\frac{(x + y)}{-1(x - y)}=(\frac{1}{-1})(\frac{(x + y)}{(x - y)})=(-1)(\frac{1}{2})=-\frac{1}{2}\)

Answer: B
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generis
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Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) = [#permalink] If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =   Updated on: 29 Apr 2019, 15:00
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Bunuel wrote:
If \(\frac{x + y}{x − y} = \frac{1}{2}\), then \(\frac{xy + x^2}{xy − x^2}=\)


(A) –4.2

(B) –1/2

(C) 1.1

(D) 3

(E) 5.3

Method I - Algebra

\(\frac{xy + x^2}{xy − x^2}\) =

\(\frac{x (y + x)}{x (y - x)}\) =

\(\frac{(y + x)}{(y - x)}\)

\((-1)*\frac{(y + x)}{(y - x)}\) =

- \(\frac{(x + y)}{(x - y)}\)

Given \(\frac{x + y}{x − y} = \frac{1}{2}\), then

- \(\frac{(x + y)}{(x - y)}\) = - \(\frac{1}{2}\)

Method II - assign values derived from first equation, plug into second equation

\(\frac{x + y}{x − y}\) = \(\frac{1}{2}\) Cross multiply:
\(2 (x + y) = (x - y)\)
\(2x + 2y = x - y\)
\(x = -3y\)

Let x = -6 and y = 2, plug into second equation \(\frac{xy + x^2}{xy − x^2}=\)

\(\frac{-12 + 36}{- 12 - 36}\)

= - \(\frac{24}{48}\) or - \(\frac{1}{2}\)

Answer B

Originally posted by generis on 01 Jun 2017, 14:26.
Last edited by generis on 29 Apr 2019, 15:00, edited 3 times in total.
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Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) = [#permalink] If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =   01 Jun 2017, 14:29
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Bunuel wrote:
If \(\frac{x + y}{x − y} = \frac{1}{2}\), then \(\frac{xy + x^2}{xy − x^2}=\)

(A) –4.2

(B) –1/2

(C) 1.1

(D) 3

(E) 5.3


Taking x as common from the fraction; \(\frac{xy + x^2}{xy − x^2}\)
\(\frac{x(y + x)}{x(y - x)}\)
Cancelling out "x" we get = \(\frac{x+y}{-(x-y)}\)

Given; \(\frac{x + y}{x − y} = \frac{1}{2}\)
Therefore ; \(\frac{x+y}{-(x-y)}\) = - \(\frac{1}{2}\)
Answer B...
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Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) = [#permalink] If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =   07 Jun 2017, 04:43
(xy + x^2)/(xy-x^2)
= x(y+x)/x(y-x)
= (y+x)/(y-x)
= -(x+y)/(x-y) = -1/2

Option B should be the correct answer.
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Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) = [#permalink] If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =   07 Jun 2017, 09:27
(xy+x^2)/(xy-x^2)= (y+x)/(y-x)= -((x+y)/(x-y))= -1/2
Answer- B
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Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) = [#permalink] If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =   10 Jun 2017, 07:30
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Bunuel wrote:
If \(\frac{x + y}{x − y} = \frac{1}{2}\), then \(\frac{xy + x^2}{xy − x^2}=\)


(A) –4.2

(B) –1/2

(C) 1.1

(D) 3

(E) 5.3


Let’s simplify (xy + x^2)/(xy - x^2):

x(y + x)/[x(y - x)]

We know x cannot equal zero (because (x + y)/(x - y) will not equal 1/2); therefore we can cancel the x:

(x + y)/(y - x)

(x + y)/(x - y) * -1

½ * -1 = -½

Answer: B
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Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) = [#permalink] If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =   27 Aug 2017, 23:46
Take the x from the numerator and denominator and -1 from the denominator to get the given condition.

-1*(x+y)/(x-y)= -1/2

Hence Ans:B
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Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) = [#permalink]
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