Which statement best reflects the solution(s) of the equation?
1/x-1 + 2/x = x/x-1
a. There is only one solution: x = 1. The solution x = 2 Is an extraneous solution.
b. There is only one solution: x = 2. The solution x = 0 is an Extraneous solution.
c. There is only one solution: x = 2. The solution x = 1 is an extraneous solution.
d. There are two solutions: x = 1 and x = 2.
1 / [ x - 1 ] + 2 /x = x / [ x - 1]
get a common denominator on both sides
[ x + 2 ( x - 1) ] / [ x (x - 1)] = x^2 / [ x (x - 1} ]
[3x - 2 ] / [ x^2 - x ] = x^2 / [ x^2 - x ]
Solve for the numerators
3x - 2 = x^2 rearrange as
x^2 - 3x + 2 = 0 factor
(x - 2) ( x - 1) = 0 set each factor to 0 and solve for x and we get the possible solutions
x = 2 or x =1
Reject the second because it makes an original denominator = 0 [ extraneous solution ]
"C" is correct