A student solves the following equation for all possible values of x: 8/x+2 = 2/x-4 His solution is as follows:
Step 1: 8 (x - 4) = 2 (x + 2)
Step 2: 4 (x - 4) = (x + 2)
Step 3: 4x - 16 = x + 2
Step 4: 3x = 18
Step 5: x = 6
He determines that 6 is an extraneous solution because the difference of the numerators is 6, so the 6s cancel to 0. Which best describes the reasonableness of the student's solution?
a) His solution for x is correct and his explanation of the extraneous solution is reasonable.
b) His solution for x is correct, but in order for 6 to be an extraneous solution, both denominators have to result in 0 when 6 is substituted for x.
c) His solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.
b) His solution for x is incorrect. When solved correctly, there are no extraneous solutions.
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