Question

Simplify1 19 х1 181 x. (2 points)O x+9909X +9O *+99x9xX+9

Answer 1

So, we're going to simplify:

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

For this, we could sum the fractions in the numerator, and the denominator, first:

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

We could rewrite the previous fraction as:

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

And, finally:

`(9x(x-9))/((x+9)(x-9))=(9x)/(x+9)`