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# For x different from 2 and

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For x different from 2 and [#permalink]  04 Sep 2019, 08:46
Expert's post
00:00

Question Stats:

94% (02:08) correct 5% (00:00) wrong based on 17 sessions
For $$x \neq 2$$ and $$x \neq 3$$ , $$\frac{-2}{x-2} + \frac{x}{x-3}=$$

A. $$1$$

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

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

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

E. $$\frac{x^2-4x+6}{(x-2)(x-3)}$$
[Reveal] Spoiler: OA

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GRE Instructor
Joined: 10 Apr 2015
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Kudos [?]: 3128 [1] , given: 54

Re: For x different from 2 and [#permalink]  04 Sep 2019, 09:05
1
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Expert's post
Carcass wrote:
For $$x \neq 2$$ and $$x \neq 3$$ , $$\frac{-2}{x-2} + \frac{x}{x-3}=$$

A. $$1$$

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

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

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

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

GIVEN: $$\frac{-2}{x-2} + \frac{x}{x-3}=$$

Rewrite with common denominators: $$\frac{(-2)(x-3)}{(x-2)(x-3)} + \frac{(x)(x-2)}{(x-3)(x-2)}$$

Simplify numerators: $$\frac{-2x+6}{(x-2)(x-3)} + \frac{x^2-2x}{(x-3)(x-2)}$$

Combine fractions: $$\frac{(-2x+6)+(x^2-2x)}{(x-2)(x-3)}$$

Simplify numerator: $$\frac{x^2-4x+6}{(x-2)(x-3)}$$

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

Re: For x different from 2 and   [#permalink] 04 Sep 2019, 09:05
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