Answer:
x = 2 + sqrt(6) or x = 2 - sqrt(6)
Step-by-step explanation by completing the square:
Solve for x:
0 = x - (x + 2)/(x - 3)
0 = x - (x + 2)/(x - 3) is equivalent to x - (x + 2)/(x - 3) = 0:
x - (x + 2)/(x - 3) = 0
Bring x - (x + 2)/(x - 3) together using the common denominator x - 3:
(x^2 - 4 x - 2)/(x - 3) = 0
Multiply both sides by x - 3:
x^2 - 4 x - 2 = 0
Add 2 to both sides:
x^2 - 4 x = 2
Add 4 to both sides:
x^2 - 4 x + 4 = 6
Write the left hand side as a square:
(x - 2)^2 = 6
Take the square root of both sides:
x - 2 = sqrt(6) or x - 2 = -sqrt(6)
Add 2 to both sides:
x = 2 + sqrt(6) or x - 2 = -sqrt(6)
Add 2 to both sides:
Answer: x = 2 + sqrt(6) or x = 2 - sqrt(6)