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Retired Moderator
Joined: 10 Apr 2015
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If x is 2 greater than the reciprocal of y+2,
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29 Jul 2019, 10:40
29 Jul 2019, 10:40
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If x is 2 greater than the reciprocal of y+2, then what the value of y in terms of x?
A) \(\frac{5+2x}{2-x}\)
B) \(\frac{5+2x}{x-2}\)
C) \(\frac{5-2x}{x-2}\)
D) \(\frac{5-2x}{2+x}\)
E) \(\frac{5x+2}{2-x}\)
A) \(\frac{5+2x}{2-x}\)
B) \(\frac{5+2x}{x-2}\)
C) \(\frac{5-2x}{x-2}\)
D) \(\frac{5-2x}{2+x}\)
E) \(\frac{5x+2}{2-x}\)
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x is 2 greater than the reciprocal of y+2,
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29 Jul 2019, 15:37
29 Jul 2019, 15:37
GreenlightTestPrep wrote:
If x is 2 greater than the reciprocal of y+2, then what the value of y in terms of x?
A) \(\frac{5+2x}{2-x}\)
B) \(\frac{5+2x}{x-2}\)
C) \(\frac{5-2x}{x-2}\)
D) \(\frac{5-2x}{2+x}\)
E) \(\frac{5x+2}{2-x}\)
A) \(\frac{5+2x}{2-x}\)
B) \(\frac{5+2x}{x-2}\)
C) \(\frac{5-2x}{x-2}\)
D) \(\frac{5-2x}{2+x}\)
E) \(\frac{5x+2}{2-x}\)
GIVEN: x is 2 greater than the reciprocal of y+2
We can write: \(x=\frac{1}{y+2} + 2\)
Multiply both sides by \(y+2\) to get: \(x(y+2)=1 + 2(y+2)\)
Expand to get: \(xy+2x=1+2y+4\)
Simplify to get: \(xy+2x=5+2y\)
Subtract 2y from both sides to get: \(xy+2x-2y=5\)
Subtract 2x from both sides to get: \(xy-2y=5-2x\)
Factor the left side to get: \(y(x-2)=5-2x\)
Divide both sides by \(x-2\)to get: \(y=\frac{5-2x}{x-2}\)
Answer: C
Cheers,
Brent
gmatclubot
Re: If x is 2 greater than the reciprocal of y+2, [#permalink]
29 Jul 2019, 15:37
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