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Question 580754: I am helping my son with SAT test taking skills. I have done what I can to look at the problem but I do not understand a part of it either!
The problem reads:
The equation x / x+2 + 3x+2 / x^2 + 2x = 3 / x has how many integer solutions?
The solutions says:
Find LCD = (x)(x+2). Multiply so all terms have common denominator.... [no problem there]. Eliminate denominators [again no problem] and solve for x,
x^2 + 3x + 2 = 3x +2 [call this A], and x^2 -4 =0 [call this B], and (x+2)(x-2)=0 [call this C]. [and then it goes on]
The problem is getting from the A to B. Once to B there is no problem with factoring.
He understands--as do I--how to factor from B to C--but how did the solution go from A to B? the x^2-4=0 just seems so odd.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The equation x / x+2 + 3x+2 / x^2 + 2x = 3 / x has how many integer solutions?
The solutions says:
Find LCM = (x)(x+2).
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x/(x+2) + (3x+2)/(x(x+2)) = 3/x
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Multiply thru by the LCM
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x^2 + 3x+2 = 3(x+2)
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x^2 + 3x + 2 = 3x + 6
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x^2 -4 = 0
(x-2)(x+2) = 0
Possible solution: x = 2 or x = -2
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But x cannot be -2 as that would make the denominator
of the original problem be zero.
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Only solution: x = 2
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Cheers,
Stan H.
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