Question

x/x-6÷x+6/xwhat is the quotient of the rational expressions

Answer 1

we want to divide

$\frac{x}{x-6}\div\text{ }\frac{x+6}{x}$

That is equivalent to say:

What we do next is multiply the extremes and multiply the expressions that are in the middle, like this:

that is equivalent to say:

$\frac{(x\text{ )(x)}}{(x-6)(x+6)}\text{ = }\frac{x^2}{x^2-6^2}$

so the correct answer is: the quotient of the rational expressions is:

$\frac{x}{x-6}\div\text{ }\frac{x+6}{x}\text{ = }\frac{x^2}{x^2-6^2}\text{ = }\frac{x^2}{x^2-36^{}}$