Question

(Multiple Choice, 20 pts)

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

A. x = 0; x = 3 is an extraneous solution
B. x = 3; x = 0 is an extraneous solution
C. x = 0; x = −3 is an extraneous solution
D. x = −3; x = 0 is an extraneous solution

Answer 1

x = -3, x = 0 is a extraneous solution

Explanation:

the person above is correct

Answer 2

x = -3, x = 0 is a extraneous solution

Explanation:

Step 1: Cross-multiply

3x² = 4x² + 3x

Step 2: Isolate x's

0 = x² + 3x

Step 3: Factor

0 = x(x + 3)

Step 4: Find roots

x = 0, -3

Step 5: Double check work

Plug in both to see if they both work. Only x = 0 should be extraneous. We now have our answer!