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- RealProLv 710 months ago
1 / (u-1) - 1 / (u+1)

= (u + 1 - u + 1) / (u^2 - 1)

= 2 / (u^2 - 1)

Let's start with u = √x

1 / (√x-1) - 1/(√x+1) = 2 / (x - 1)

2/(x-1) - 2/(x+1) = 2[1/(x-1) - 1/(x+1)]

= 2 * 2/(x^2 - 1)

= 4 / (x^2 - 1)

4 / (x^2 - 1) - 4 / (x^2 + 1) = 8 / (x^4 - 1)

8 / (x^4 - 1) - 8 / (x^4 + 1) = 16 / (x^8 - 1)

16 / (x^8 - 1) = 1/5

x^8 = 16*5 + 1

We take only the positive root because of √x

x = 81^(1/8) = 9^(1/4) = 3^(1/2) = 1.73205...

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