Question

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

Answer 1

`(9x)/(x+9)`

Explanation:

we have to simplify:

`((1)/(9)-(1)/(x))/((1)/(81)-(1)/(x^2))\\ \\\\=((x-9)/(9x))/((x^2-81)/(81x^2))\\ \\\\=9x* (x-9)/(x^2-81)\\ \\\\=9x* (x-9)/((x-9)(x+9))\\ \\\\=(9x)/(x+9)`

Answer 2

`((1)/(9)-(1)/(x))/((1)/(81)-(1)/(x^2))=((x-9)/(9x))/((x^2-81)/(81x^2))=(81x^2(x-9))/(9x(x-9)(x+9))=(9x)/(x+9)`