sqrt(3x+1)-sqrt(x-1)=2

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Solution for sqrt(3x+1)-sqrt(x-1)=2 equation:


Simplifying
sqrt(3x + 1) + -1sqrt(x + -1) = 2

Reorder the terms:
qrst(1 + 3x) + -1sqrt(x + -1) = 2
(1 * qrst + 3x * qrst) + -1sqrt(x + -1) = 2
(1qrst + 3qrstx) + -1sqrt(x + -1) = 2

Reorder the terms:
1qrst + 3qrstx + -1qrst(-1 + x) = 2
1qrst + 3qrstx + (-1 * -1qrst + x * -1qrst) = 2
1qrst + 3qrstx + (1qrst + -1qrstx) = 2

Reorder the terms:
1qrst + 1qrst + 3qrstx + -1qrstx = 2

Combine like terms: 1qrst + 1qrst = 2qrst
2qrst + 3qrstx + -1qrstx = 2

Combine like terms: 3qrstx + -1qrstx = 2qrstx
2qrst + 2qrstx = 2

Solving
2qrst + 2qrstx = 2

Solving for variable 'q'.

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

Reorder the terms:
-2 + 2qrst + 2qrstx = 2 + -2

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + qrst + qrstx) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + qrst + qrstx)' equal to zero and attempt to solve: Simplifying -1 + qrst + qrstx = 0 Solving -1 + qrst + qrstx = 0 Move all terms containing q to the left, all other terms to the right. Add '1' to each side of the equation. -1 + qrst + 1 + qrstx = 0 + 1 Reorder the terms: -1 + 1 + qrst + qrstx = 0 + 1 Combine like terms: -1 + 1 = 0 0 + qrst + qrstx = 0 + 1 qrst + qrstx = 0 + 1 Combine like terms: 0 + 1 = 1 qrst + qrstx = 1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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