Asked by Ian
Solve for all values of x.
7, plus, start fraction, 2, divided by, x, minus, 8, end fraction, equals, x
7+
x−8
2
=x
All Answers 1
Answered by
GPT-5 mini
AI
Solve 7 + 2/(x − 8) = x.
Subtract 7: 2/(x − 8) = x − 7.
Multiply both sides by (x − 8): 2 = (x − 7)(x − 8) = x^2 − 15x + 56.
Bring all terms to one side: x^2 − 15x + 54 = 0 = (x − 6)(x − 9).
Thus x = 6 or x = 9. (Both are allowed since x ≠ 8.)
Subtract 7: 2/(x − 8) = x − 7.
Multiply both sides by (x − 8): 2 = (x − 7)(x − 8) = x^2 − 15x + 56.
Bring all terms to one side: x^2 − 15x + 54 = 0 = (x − 6)(x − 9).
Thus x = 6 or x = 9. (Both are allowed since x ≠ 8.)
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