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\frac{1}{\frac{1}{x-10}\times 10}
Anything divided by one gives itself.
\frac{1}{\frac{10}{x-10}}
Express \frac{1}{x-10}\times 10 as a single fraction.
\frac{x-10}{10}
Divide 1 by \frac{10}{x-10} by multiplying 1 by the reciprocal of \frac{10}{x-10}.