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# If x ≠ 0 and x - (2- x^2)/x = y/x, then y =

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Math Expert
Joined: 02 Sep 2009
Posts: 51280
If x ≠ 0 and x - (2- x^2)/x = y/x, then y =  [#permalink]

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13 Dec 2015, 05:12
00:00

Difficulty:

15% (low)

Question Stats:

74% (01:11) correct 26% (01:10) wrong based on 100 sessions

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If x ≠ 0 and x - (2- x^2)/x = y/x, then y =

A. − 2 − 3x^2
B. x^2 − 2
C. 2x^2 − 2
D. x − 2 − x^2
E. x − 2 + x^2

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Re: If x ≠ 0 and x - (2- x^2)/x = y/x, then y =  [#permalink]

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13 Dec 2015, 05:40
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Bunuel wrote:
If x ≠ 0 and $$x - \frac{(2- x^2)}{x}$$ = $$\frac{y}{x}$$, then y =

$$x - \frac{(2- x^2)}{x}$$ = $$\frac{y}{x}$$

So,$$\frac{x^2 - (2 - x^2)}{x}$$ = $$\frac{y}{x}$$

Or,$$x^2 - 2 + x^2$$ = $$y$$

Or, $$y$$ = $$2x^2 - 2$$

Answer is (C)

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Re: If x ≠ 0 and x - (2- x^2)/x = y/x, then y =  [#permalink]

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13 Dec 2015, 08:40
Bunuel wrote:
If x ≠ 0 and x - (2- x^2)/x = y/x, then y =

A. − 2 − 3x^2
B. x^2 − 2
C. 2x^2 − 2
D. x − 2 − x^2
E. x − 2 + x^2

Multiply the whole expression by X:$$x^2-2+x^2=y$$->$$y=2x^2-2$$, Asnwer C
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Re: If x ≠ 0 and x - (2- x^2)/x = y/x, then y =  [#permalink]

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15 Dec 2015, 16:02
Hi All,

This question can be solved by TESTing VALUES. The answer choices are also written in such a way that you can avoid doing some of the math involved within them.

We're told that x ≠ 0 and x - (2- x^2)/x = y/x. We're asked for the value of y.

IF.... X = 3
3 - (2 - 3^2)/3 = y/3

9/3 - (-7/3) = y/3

Multiply everything by 3....
9 - (-7) = y
16 = y

So we're looking for an answer that equals 16 when x = 3...

Answer A) − 2 − 3x^2 This will be NEGATIVE, so no need to calculate it.
Answer B) x^2 − 2 = 7. NOT a match.
Answer C) 2x^2 − 2 = 16. This IS a match.
Answer D) x − 2 − x^2 This will be NEGATIVE, so no need to calculate it.
Answer E) x − 2 + x^2 = 10. NOT a match.

Final Answer:

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Re: If x ≠ 0 and x - (2- x^2)/x = y/x, then y =  [#permalink]

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13 Apr 2016, 02:08
this problem can be solved easily by simplification.Solve the L.H.S.and y reduces to 2x^2 - 2
correct answer - C
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Re: If x ≠ 0 and x - (2- x^2)/x = y/x, then y =  [#permalink]

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27 Feb 2018, 13:05
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Re: If x ≠ 0 and x - (2- x^2)/x = y/x, then y = &nbs [#permalink] 27 Feb 2018, 13:05
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# If x ≠ 0 and x - (2- x^2)/x = y/x, then y =

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