SOLUTION: Please help me solve this problem: Which of the following equations have extraneous solutions? a)(1/(x-1))+(x/5)=(x/(x-1)) b)(x+3)/(x+5)=(2x+8)/(x+5) c)x-(2/x)=-1 d)3/(x+7)=5/

Question 1042819: Please help me solve this problem:
Which of the following equations have extraneous solutions?
a)(1/(x-1))+(x/5)=(x/(x-1))
b)(x+3)/(x+5)=(2x+8)/(x+5)
c)x-(2/x)=-1
d)3/(x+7)=5/(x-2)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Which of the following equations have extraneous solutions?
a)(1/(x-1))+(x/5)=(x/(x-1))
Multiply thru by 5(x-1) to get:
5 + x(x-1) = 5x
5 + x^2 - x = 5x
x^2 - 6x + 5 = 0
(x-5)(x-1) = 0
x = 1 is extraneous because x-1 is in the denominator:
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b)(x+3)/(x+5)=(2x+8)/(x+5)
x+3 = 2x+8
x = -5 is extraneous because x+5 is in the denominator
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c)x-(2/x)=-1
x^2 - 2 = -x
x^2 + x - 2 = 0
(x+2)(x-1) = 0
x = -2 or x = 1
No extraneous zeroes
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d)3/(x+7)=5/(x-2)
3x-6 = 5x+35
2x = -41
x = -20.5
No extraneous
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Cheers,
Stan H.
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