Question

What is the quotient in simplest form? State any restrictions on the variable.see image

Answer 1

we have the expression

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

Multiply in cross

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

Simplify

z^2-4=(z+2)(z-2) -----> difference of squares

z^2+z-12=(z+4)(z-3)

substitute in the above expression

`(\mleft(z+2\mright)\mleft(z-2\mright)\mleft(z+4\mright)\mleft(z-3\mright))/((z-3)(z+2))`

Simplify

`(z-2)(z+4)`