sqrt(x+1)-sqrt(x-1)=1

Solution for sqrt(x+1)-sqrt(x-1)=1 equation:

Simplifying
sqrt(x + 1) + -1sqrt(x + -1) = 1

Reorder the terms:
qrst(1 + x) + -1sqrt(x + -1) = 1
(1 * qrst + x * qrst) + -1sqrt(x + -1) = 1
(1qrst + qrstx) + -1sqrt(x + -1) = 1

Reorder the terms:
1qrst + qrstx + -1qrst(-1 + x) = 1
1qrst + qrstx + (-1 * -1qrst + x * -1qrst) = 1
1qrst + qrstx + (1qrst + -1qrstx) = 1

Reorder the terms:
1qrst + 1qrst + qrstx + -1qrstx = 1

Combine like terms: 1qrst + 1qrst = 2qrst
2qrst + qrstx + -1qrstx = 1

Combine like terms: qrstx + -1qrstx = 0
2qrst + 0 = 1
2qrst = 1

Solving
2qrst = 1

Solving for variable 'q'.

Move all terms containing q to the left, all other terms to the right.

Divide each side by '2rst'.
q = 0.5r-1s-1t-1

Simplifying
q = 0.5r-1s-1t-1