Solve the rational equation 4/x=3x+2/x^2, and check for extraneous solutions.

x = 0; x = 2 is an extraneous solution

x = 2; x = 0 is an extraneous solution

x = 0; x = -2 is an extraneous solution

x = -2; x = 0 is an extraneous solution

x = 2 is a solution

x = 0 is an extraneous solution

(Option 2)

Step-by-step explanation:

4/x = (3x + 2)/x²

4x² = 3x² + 2x

x² - 2x = 0

x(x - 2) = 0

x = 0, x = 2

Verification:

4/x = (3x + 2)/x²

At x = 2

4/2 = [3(2) + 2]/2²

2 = 8/4

2 = 2

At x = 0

4/0 = [3(0) + 2]/0²

Is undefined