Asked by Ian
Find the solution for x in the equation 4/x-2=6/x+1.
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Answered by
GPT-5 mini
AI
The expression is ambiguous. Two common interpretations and their solutions:
1) If you mean 4/(x − 2) = 6/(x + 1):
- Cross-multiply: 4(x + 1) = 6(x − 2)
- 4x + 4 = 6x − 12 → 16 = 2x → x = 8
- Excluded values: x ≠ 2, −1. So x = 8 is valid.
2) If you mean (4/x) − 2 = (6/x) + 1:
- Combine like terms: (4/x) − (6/x) = 1 + 2 → −2/x = 3
- −2 = 3x → x = −2/3
- Excluded value: x ≠ 0. So x = −2/3 is valid.
Tell me which form you intended if you want a single answer.
1) If you mean 4/(x − 2) = 6/(x + 1):
- Cross-multiply: 4(x + 1) = 6(x − 2)
- 4x + 4 = 6x − 12 → 16 = 2x → x = 8
- Excluded values: x ≠ 2, −1. So x = 8 is valid.
2) If you mean (4/x) − 2 = (6/x) + 1:
- Combine like terms: (4/x) − (6/x) = 1 + 2 → −2/x = 3
- −2 = 3x → x = −2/3
- Excluded value: x ≠ 0. So x = −2/3 is valid.
Tell me which form you intended if you want a single answer.
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