The easy way to do this problem is to start with the choices. What we will do is to expand the choices back to their original form.
A. (x+5 ) + -2/x-1 = 0
Multiplying both sides by x – 1
(x-1)(x+5) - 2 = 0
x^2 + 5x – x – 5 - 2= 0
x^2 + 4x – 7 = 0
Multiplying both sides by (1/x-1)
x^2 + 4x – 7 / x-1
B. (x-1) + 6/x-1 = 0
Multiplying both sides by x – 1
(x-1)(x-1) + 6 = 0
x^2 –x –x +1 + 6 = 0
x^2 – 2x + 7 = 0
Multiplying both sides by (1/x-1)
x^2 - 2x + 7 / x-1
C. (2x+1) + -6/x-1 = 0
Multiplying both sides by x – 1
(x-1)( 2x+1) - 6 = 0
2x^2 + x – 2x -1 – 6 = 0
2x^2 – x – 7 = 0
Multiplying both sides by (1/x-1)
2x^2 – x – 7 /x-1
D. (2x-1) + 6/x-1
Multiplying both sides by x – 1
(x-1)(2x-1) + 6 = 0
2x^2 - x – 2x +1 + 6 = 0
2x^2 – 3x + 7 = 0
Multiplying both sides by (1/x-1)
2x^2 – 3x + 7 /x-1