+130085 1 / [ x - 1 ] + 2 / x = x / [ x - 1 ]
Subtract the first fraction from both sides
2 / x = x / [ x - 1 ] - 1 / [ x - 1 ]
2 / x = [ x - 1] / [ x - 1] cross-multiply
2[ x - 1 ] = x [ x - 1 ] simplify
2x - 2 = x^2 - x subtract 2x from both sides....add 2 to both sides
x^2 - 2x - x + 2 = 0 simplify
x^2 - 3x + 2 = 0 factor
(x - 2) ( x - 1) = 0
Setting each factor to 0 and soving for x produces x = 2 or x = 1
The second solution makes two denominators inthe original problem = 0
So....x = 2 is the only solution
The third answer is correct
