Question

Perform the indicated operations and reduce to lowest terms. Assume that no denominator has a value of zero. ​

Answer 1

`(x)/(9)`

Explanation:

Given

`(x^2 - 9)/(9x + 27) / (x - 3)/(x)`

Required

Solve

`(x^2 - 9)/(9x + 27) / (x - 3)/(x)`

Change the division to multiplication

`(x^2 - 9)/(9x + 27) * (x)/(x - 3)`

Apply difference of 2 squares

`((x - 3)(x+3))/(9x + 27) * (x)/(x - 3)`

Cancel out x - 3

`(x+3)/(9x + 27) * (x)/(1)`

Factorize 9x + 27

`(x+3)/(9(x + 3)) * (x)/(1)`

Cancel out x + 3

`(1)/(9) * (x)/(1)`

Finally, this gives:

`(x)/(9)`