Rational Equation

5 = -x-5/x+5 or,

x^2 = -5  (for x!=0)

5=(1/x-1)-(x+6/x-6)      add (x + 6)/ (x - 6) to both sides

5 + (x + 6) / (x - 6)    =  (1)/ (x - 1)       simplify the left side

[5(x - 6) + (x + 6)]/ (x - 6)  = 1 / (x - 1)

[5x - 30 + x + 6] / (x - 6)   = 1 / (x - 1)

[6x - 24] / (x - 6)   = 1 / (x - 1)   cross-multiply

[6x - 24][x - 1] = x - 6        expand on the left side

6x^2 - 30x + 24  = x - 6      subtract [x - 6] from both sides

6x^2 - 31x +30 = 0    this will not factor

The solutions using the Quadratic Formula  are  x =     [31 +/- sqrt(241)] / 12