Question

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

Answer 1

The given expression:

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

Apply the fraction rule:

`\begin{gathered} ((a)/(b))/((c)/(d))=(a\cdot \:d)/(b\cdot \:c) \\ =(\left(z^2-4\right)\left(z^2+z-12\right))/(\left(z-3\right)\left(z+2\right)) \end{gathered}`

Cancel out (z - 3)(z + 2):

`=\left(z-2\right)\left(z+4\right)`

Therefore,

`(z-2)(z+4)=z^2+2z-8`

Therefore, the quotient in simplest form is

`z^2+2z-8`

The restrictions are that none of the cancelled factors can be 0, so z ≠ 3 and z ≠- 4.