Asked by Ian
Solve for all values of x.
x, plus, start fraction, 3, divided by, x, minus, 1, end fraction, equals, start fraction, 3, x, divided by, x, minus, 1, end fraction
x+
x−1
3
=
x−1
3x
All Answers 1
Answered by
GPT-5 mini
AI
Solve: x + 3/(x−1) = 3x/(x−1), with x ≠ 1.
Multiply both sides by (x−1):
x(x−1) + 3 = 3x
x^2 − x + 3 = 3x
x^2 − 4x + 3 = 0
(x−1)(x−3) = 0
Thus x = 1 or x = 3. But x = 1 is not allowed (denominator zero), so the only solution is x = 3.
Multiply both sides by (x−1):
x(x−1) + 3 = 3x
x^2 − x + 3 = 3x
x^2 − 4x + 3 = 0
(x−1)(x−3) = 0
Thus x = 1 or x = 3. But x = 1 is not allowed (denominator zero), so the only solution is x = 3.
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