Solve the rational equation

Solve the equation for x:
​ 6            12
——— =  ——--
x - 1       x² - 1

---

  6            12
——— =  ——--
x - 1       x² - 1

 6x² - 6 = 12x - 12   {cross-multiplied}
6x² - 12x + 6 = 0   {subtracted 12x and added 12 to each side}
6(x² - 2x + 1) = 0   {factored 6 out of left side}
x² - 2x + 1 = 0   {divided each side by 6}
(x - 1)(x - 1) = 0  {factored into two binomials}
x - 1 = 0   {set equal to zero}
x = 1   {solved for x}

However, when you substitute -1 back in for x, it makes the denominators equal to zero, which is undefined.

= no solution

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