Find all real solutions Be sure to check for extraneous solu

Find all real solutions. Be sure to check for extraneous solutions -z^3 + 4z/z^2 - 9 = 4z

Solution

(-z³ +4z)/(z² -9) = 4z

==> (-z³ +4z) = 4z(z² -9)

==> -z³ + 4z = 4z¹⁺² - 36z                  since a^m * aⁿ = a^m+n

==> -z³ + 4z = 4z³ - 36z     

==> -z³ -4z³ + 4z + 36z = 0

==> -5z³ + 40z = 0

==> -z³ + 8z = 0

==> z(-z² + 8) = 0

==> z = 0 , z² = 8

==> z = 0 , z = 22 , -22

Hence z = 0 , 22 , -22