Question

What is the quotient in simplest form? State any restrictions on the variable. Show all work.

(x^2-4)/(x-3) divided by (x+2)/(x^2+x-12)

Answer 1

(x-2) (x+4)

Explanation:

(x^2-4) (x^2+x-12)

= --------------- * --------------- ; x ≠3 or x ≠ -2

(x-3) (x+2)

(x+2)(x-2) (x-3)(x+4)

= --------------- * ---------------

(x-3) (x+2)

= (x-2) (x+4)

Answer 2

`(z-2)/(z+4),z\\e-4`

Explanation:

The given quotient is

`(z^2-4)/(z-3)/ (z+2)/(z^2+z-12)`

Multiply by the reciprocal of the second fraction;

`(z^2-4)/(z-3)* (z^2+z-12)/(z+2)`

Factorize the numerators;

`(z^2-2^2)/(z-3)* (z^2+4z-3z-12)/(z+2)`

`((z-2)(z+2))/(z-3)* (z(z+4)-3(z+4))/(z+2)`

`((z-2)(z+2))/(z-3)* ((z-3)(z+4))/(z+2)`

Cancel out the common factors;

`((z-2)(1))/(1)* ((1)(z+4))/(1)`

`(z-2)/(z+4),z\\e-4`