SOLUTION: Find all x for which x^3-x^2-x+1 /x^3-x^2+x-1 = 0. Please can someone help me? I'm not even sure if this problem belongs in this section, let alone, how to do it. Thanks!!!
Question 180216: Find all x for which x^3-x^2-x+1 /x^3-x^2+x-1 = 0. Please can someone help me? I'm not even sure if this problem belongs in this section, let alone, how to do it. Thanks!!! Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Find all x for which x^3-x^2-x+1 /x^3-x^2+x-1 = 0.
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Multiply both sides by the denominator to get:
x^3-x^2-x+1 = 0
Factor to get:
(x^2)(x-1) - (x-1) = 0
Factor again:
(x-1)(x^2-1) = 0
Factor again:
(x-1)(x-1)(x+1) = 0
Solutions: x = 1, or x = -1
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But x=1 is extraneous as it makes the original denominator = 0
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Only solution: x = -1
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Cheers,
Stan H.
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