Question 374977
{{{(t-2)/(t-1)}}} = {{{(t+17)/(t^(2)-1)}}} - {{{1/(t+1)}}}
Factoring (t^2-1) as the difference of squares, reveals the common denominator of (t-1)(t+1 
{{{(t-2)/(t-1)}}} = {{{(t+17)/((t+1)(t-1))}}} - {{{1/(t+1)}}}
:
Multiply thru by (t+1)(t-1) and you have:
(t+1)(t-2) = t + 17 - (t-1)
:
FOIL the left side remove the brackets on the right side
t^2 - t - 2 = t + 17 - t + 1
:
t^2 - t - 2 = 18
:
t^2 - t - 2 - 18 = 0
:
t^2 - t - 20 = 0
Factors to
(x-5)(x+4) = 0
two solutions
x = -4
x = +5
:
You can check both solutions in the original problem