Question

How do you express the quotient of `(x^2-4)/(x^3+7x^2) -: (x^3-x^2-6x)/(x^2+4x-21)`? in simplest form?

Answer 1

You must first transform into a multiplication and then factor to see what you can eliminate.

Explanation:

To transform a fractional division into a multiplication, you have to inverse the numerator and the denominator of the second fraction.

`(x^2 - 4)/(x^3 + 7x^2) xx (x^2 + 4x - 21)/(x^3 - x^2 - 6x)`

`((x + 2)(x - 2))/(x^2(x + 7)) xx ((x + 7)(x - 3))/(x(x - 3)(x + 2))`

Since `a/a = 1, a =` all real numbers, we can proceed by eliminating factors that appear in the numerator and the denominator.

We are left with `(x- 2)/x^3`