Solve the following equation: 1/(x-1) + 1/(x+1) = 18

First, we'll move all terms to one
side:

1/(x-1) + 1/(x+1) - 18 = 0

Now,
we'll calculate the least common denominator for adding the
ratios:

LCD = (x-1)(x+1)

We notice that
the result of the product is the difference of squares:

(x-1)(x+1) 
= x^2 - 1

We'll re-write the
equation:

x + 1 + x - 1 - 18(x^2 - 1) =
0

We'll remove the brackets and we'll combine and eliminate like
terms:

2x - 18x^2 + 18 = 0

We'll divide
by -2 and we'll re-arrange the terms:

9x^2 - x - 9 =
0

We'll apply the quadratic formula:

x1
= [1 + sqrt(1 + 324)]/18

x1 =
(1+5sqrt13)/18

x2 =
(1-5sqrt13)/18

Since the roots are
different from the values 1 and -1, we'll accept them.