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Simplifying ln(2x2 + -4) + -1ln(x + 1) + -1ln(x + -1) = 0 Reorder the terms: ln(-4 + 2x2) + -1ln(x + 1) + -1ln(x + -1) = 0 (-4 * ln + 2x2 * ln) + -1ln(x + 1) + -1ln(x + -1) = 0 (-4ln + 2lnx2) + -1ln(x + 1) + -1ln(x + -1) = 0 Reorder the terms: -4ln + 2lnx2 + -1ln(1 + x) + -1ln(x + -1) = 0 -4ln + 2lnx2 + (1 * -1ln + x * -1ln) + -1ln(x + -1) = 0 -4ln + 2lnx2 + (-1ln + -1lnx) + -1ln(x + -1) = 0 Reorder the terms: -4ln + 2lnx2 + -1ln + -1lnx + -1ln(-1 + x) = 0 -4ln + 2lnx2 + -1ln + -1lnx + (-1 * -1ln + x * -1ln) = 0 -4ln + 2lnx2 + -1ln + -1lnx + (1ln + -1lnx) = 0 Reorder the terms: -4ln + -1ln + 1ln + -1lnx + -1lnx + 2lnx2 = 0 Combine like terms: -4ln + -1ln = -5ln -5ln + 1ln + -1lnx + -1lnx + 2lnx2 = 0 Combine like terms: -5ln + 1ln = -4ln -4ln + -1lnx + -1lnx + 2lnx2 = 0 Combine like terms: -1lnx + -1lnx = -2lnx -4ln + -2lnx + 2lnx2 = 0 Solving -4ln + -2lnx + 2lnx2 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-2 + -1x + x2) = 0 Factor a trinomial. 2ln((-1 + -1x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Add 'x' to each side of the equation. -1x + x = 1 + x Combine like terms: -1x + x = 0 0 = 1 + x Simplifying 0 = 1 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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