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# For x ≠ 0 and x ≠ 3, -2/(x - 2) + x/(x - 3) =

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Math Expert
Joined: 02 Sep 2009
Posts: 62353
For x ≠ 0 and x ≠ 3, -2/(x - 2) + x/(x - 3) =  [#permalink]

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05 Sep 2019, 02:23
00:00

Difficulty:

15% (low)

Question Stats:

95% (01:11) correct 5% (01:19) wrong based on 21 sessions

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For x ≠ 0 and x ≠ 3, $$\frac{-2}{x-2} + \frac{x}{x-3}=$$

A. $$1$$

B. $$\frac{1}{x-3}$$

C. $$\frac{x-2}{2x-5}$$

D. $$\frac{-2x}{(x-2)(x-3)}$$

E. $$\frac{x^2-4x+6}{(x-2)(x-3)}$$

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Intern
Joined: 02 Sep 2019
Posts: 9
Re: For x ≠ 0 and x ≠ 3, -2/(x - 2) + x/(x - 3) =  [#permalink]

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05 Sep 2019, 11:37
Adding the fractions would be as follows:

a/b + c/d = [ad + bc] / bd

The result in this case...

[(-2)(x-3) + (x-2)(x)] / (x-2)(x-3)

[-2x + 6 + x^2 - 2x] / (x-2)(x-3)

x^2 - 4x + 6 / (x-2)(x-3)

So I would vote for E to be the answer.
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Re: For x ≠ 0 and x ≠ 3, -2/(x - 2) + x/(x - 3) =  [#permalink]

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05 Sep 2019, 11:42
Bunuel wrote:
For x ≠ 0 and x ≠ 3, $$\frac{-2}{x-2} + \frac{x}{x-3}=$$

A. $$1$$

B. $$\frac{1}{x-3}$$

C. $$\frac{x-2}{2x-5}$$

D. $$\frac{-2x}{(x-2)(x-3)}$$

E. $$\frac{x^2-4x+6}{(x-2)(x-3)}$$

On solving the equation, result comes out as : \frac{x2−4x+6}{(x−2)(x−3)}

Hope it helps.
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Unable to Give Up!
Re: For x ≠ 0 and x ≠ 3, -2/(x - 2) + x/(x - 3) =   [#permalink] 05 Sep 2019, 11:42
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