Simplify quantity 1 over 9 minus 1 over x all over 1 over 81 minus 1 over x squared.

Solution:

\( \\\frac{\frac{1}{9}-\frac{1}{x}}{\frac{1}{81}-\frac{1}{x^{2}}} \\ \\=\frac{\frac{x-9}{9x}}{\frac{x^{2}-81}{81x^{2}}} \\ \\=9x\times \frac{x-9}{x^{2}-81} \\ \\=9x\times \frac{x-9}{(x-9)(x+9)} \\ \\=\frac{9x}{x+9}\)

Therefore, by simplification we get 9x/(x + 9).

Simplify quantity 1 over 9 minus 1 over x all over 1 over 81 minus 1 over x squared.

Summary:

The quantity 1 over 9 minus 1 over x all over 1 over 81 minus 1 over x squared by simplification is 9x/(x + 9).