STEP                                                          REASON

1. Let  x = y.                                             Given

2. x^2 = yx                                                Multiplication property of equality
                                                                    (multiplying both sides by the same amount)

3. x^2 - y^2 = yx - y^2                             Subtraction property of equality
                                                                    (subtracting both sides by the same amount)

4. (x + y)( x - y) = yx - y^2                       Factoring the left side.    
                                                                      (difference of two squares)

5. (x + y)(x - y) = y(x - y).                      Factoring the right side (distributive property)

6. (x + y)(x - y)  =  y(x - y)                      Division property of equality.
     ---------------   ----------                              (dividing both sides by the same amount)
           x - y              x - y

7.   x + y = y                                              Identity property (cancel out same factor
                                                                       in numerator and denominator)

8.   y + y = y                                              Substitution principle
                                                                        (substitute y for x since x = y).

9.   2y = y                                                   Distributive property (backwards) (collecting like terms)

10.   2y =  y                                                Division property of equality (dividing both sides
        ----  ---                                                               by the same amount).
         y       y

11.   2 = 1                                                  Identity property (any number divided by itself is 1).