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\frac{\left(-\frac{1}{\left(x-1\right)^{2}}\right)\left(x-1\right)^{2}}{2}
Divide -\frac{1}{\left(x-1\right)^{2}} by \frac{2}{\left(x-1\right)^{2}} by multiplying -\frac{1}{\left(x-1\right)^{2}} by the reciprocal of \frac{2}{\left(x-1\right)^{2}}.
\frac{-1}{2}
Cancel out \left(x-1\right)^{2} and \left(x-1\right)^{2}.
-\frac{1}{2}
Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.