30 points and !

1. solve the rational equation x divided by 4 equals x squared divided by quantity x plus 2 end quantity, and check for extraneous solutions.

x = two thirds; 0 is an extraneous solution
x = 0; x = two thirds is an extraneous solution
x = 0 and x = two thirds
no solution

2. solve the rational equation 3 divided by x equals quantity 4 times x plus 3 divided by x squared, and check for extraneous solutions.

x = 0; x = 3 is an extraneous solution
x = 3; x = 0 is an extraneous solution
x = 0; x = −3 is an extraneous solution
x = −3; x = 0 is an extraneous solution

3. find the domain for the rational function f of x equals quantity x minus 1 end quantity divided by quantity x plus 3 end quantity.

(−∞, 1) (1, ∞)
(−∞, −1) (−1, ∞)
(−∞, 3) (3, ∞)
(−∞, −3) (−3, ∞)