(z^(2)-4)/(z-3) divided by (z+2)/(z^(2)+z-12)
what is the quotient in simplest form. state any restrictions on the variable. show all steps
To divide the two fractions, we multiply the first fraction by the reciprocal of the second fraction:
(z^2 - 4)/(z - 3) * (z^2 + z - 12)/(z + 2)
Factor the expressions:
=((z - 2)(z + 2)/(z - 3)) * ((z + 4)(z - 3)/(z + 2))
Next, cancel out common factors in the numerator and denominator:
=((z - 2)(z + 4))/(z + 2)
So, the quotient in simplest form is (z - 2)(z + 4) / (z + 2).
The restrictions on the variable are z cannot be equal to 3 (due to the denominator of (z - 3)) and z cannot be equal to -2 (due to the denominator of (z + 2)) as these values would result in division by zero.