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.

Guest Oct 18, 2018

#1**+1 **

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

CPhill
Oct 18, 2018