1/(x-1)^2+3/x-1-10=0

It looks like you meant 1/(x−1)^2 + 3/(x−1) − 10 = 0 (both fractions with the same denominator). If so:

• Let t = x − 1 (t ≠ 0). Then 1/t^2 + 3/t − 10 = 0.
• Multiply by t^2: 1 + 3t − 10t^2 = 0 → 10t^2 − 3t − 1 = 0.
• This factors as (5t + 1)(2t − 1) = 0, so t = −1/5 or t = 1/2.
• Therefore x = t + 1 gives x = 1 − 1/5 = 4/5 or x = 1 + 1/2 = 3/2.

Solutions: x = 4/5 or x = 3/2 (both ≠ 1).

If you meant a different expression, e.g., 1/(x−1)^2 + 3/x − 11 = 0 or 1/(x−1)^2 + 3/x − 1 − 10 = 0 interpreted differently, let me know and I’ll solve that version.