(x+a/x–a)2–5(x+a/x–a)+6=0,x≠a
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Let [(x+a)/(x-a)] = t,
So, t^2 -5t + 6 = 0.
t^2 - 3t - 2t + 6 =0.
(t - 3)×(t - 2) = 0.
t = 3 or t = 2.
Now,
t = [(x + a)/(x - a)] = 3 or 2
Case 1) t = 3,
x + a = 3x - 3a
2x = 4a
x = 2a.
Case 2)t = 2,
x + a = 2x - 2a
x = 3a.
So, t^2 -5t + 6 = 0.
t^2 - 3t - 2t + 6 =0.
(t - 3)×(t - 2) = 0.
t = 3 or t = 2.
Now,
t = [(x + a)/(x - a)] = 3 or 2
Case 1) t = 3,
x + a = 3x - 3a
2x = 4a
x = 2a.
Case 2)t = 2,
x + a = 2x - 2a
x = 3a.
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