Question

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

Answer 1

Answer:

$\frac{x}{9}$

Step-by-step explanation:

Given

$\frac{x^2 - 9}{9x + 27} \div \frac{x - 3}{x}$

Required

Solve

$\frac{x^2 - 9}{9x + 27} \div \frac{x - 3}{x}$

Change the division to multiplication

$\frac{x^2 - 9}{9x + 27} * \frac{x}{x - 3}$

Apply difference of 2 squares

$\frac{(x - 3)(x+3)}{9x + 27} * \frac{x}{x - 3}$

Cancel out x - 3

$\frac{x+3}{9x + 27} * \frac{x}{1}$

Factorize 9x + 27

$\frac{x+3}{9(x + 3)} * \frac{x}{1}$

Cancel out x + 3

$\frac{1}{9} * \frac{x}{1}$

Finally, this gives:

$\frac{x}{9}$