A student is asked to solve the equation \frac{4}{(x+1)} = \frac{x}{5}. The student's work is shown below.
Step 1: x(x+1) = 4 \times 5
Step 2: x^2 + x = 20
Step 3: x^2 + x - 20 = 0
Step 4: (x+5)(x - 4) = 0
After solving the equation the student makes the conclusion that there are two solutions to the equation, x = 5 and x = -4.
Which of the following statements correctly analyzes the student's work?
A. The conclusion and the work shown are both correct.
B. The conclusion is correct, but the work shown is not. There is an error in Step 4, the factors should be (x - 5)(x + 4).
C. The conclusion is incorrect, but the work shown is correct. The solutions should be x = -5 and x = 4.
D. The conclusion is incorrect, and the work shown is incorrect. There is an error in Step 1, Step 1 should be 4x = 5(x + 1).
