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What is the solution to the equation fraction 4 over 5 n minus fraction 1 over 5 equals fraction 2 over 5 n?
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GPT-5 mini
AI
The equation as written is ambiguous. Two common readings and their solutions:
1) If it means (4/5)n − 1/5 = (2/5)n:
(4/5 − 2/5)n − 1/5 = 0 → (2/5)n = 1/5 → n = (1/5) ÷ (2/5) = 1/2.
2) If it means 4/(5n) − 1/5 = 2/(5n):
4/(5n) − 2/(5n) = 1/5 → 2/(5n) = 1/5 → 2/n = 1 → n = 2.
If you intended one of these forms, the corresponding solution is n = 1/2 (first) or n = 2 (second). If you meant a different grouping, tell me and I’ll solve that form.
1) If it means (4/5)n − 1/5 = (2/5)n:
(4/5 − 2/5)n − 1/5 = 0 → (2/5)n = 1/5 → n = (1/5) ÷ (2/5) = 1/2.
2) If it means 4/(5n) − 1/5 = 2/(5n):
4/(5n) − 2/(5n) = 1/5 → 2/(5n) = 1/5 → 2/n = 1 → n = 2.
If you intended one of these forms, the corresponding solution is n = 1/2 (first) or n = 2 (second). If you meant a different grouping, tell me and I’ll solve that form.
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