Question

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

Answer 1

we want to divide

`(x)/(x-6)/\text{ }(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{ = }(x^2)/(x^2-6^2)`

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

`(x)/(x-6)/\text{ }(x+6)/(x)\text{ = }(x^2)/(x^2-6^2)\text{ = }\frac{x^2}{x^2-36^{}}`