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Simplifying ln(x + -1)(x + -1) + ln(x + -1)(x + 1) + ln(x + 1)(x + 1) = 0 Reorder the terms: ln(-1 + x)(x + -1) + ln(x + -1)(x + 1) + ln(x + 1)(x + 1) = 0 Reorder the terms: ln(-1 + x)(-1 + x) + ln(x + -1)(x + 1) + ln(x + 1)(x + 1) = 0 Multiply (-1 + x) * (-1 + x) ln(-1(-1 + x) + x(-1 + x)) + ln(x + -1)(x + 1) + ln(x + 1)(x + 1) = 0 ln((-1 * -1 + x * -1) + x(-1 + x)) + ln(x + -1)(x + 1) + ln(x + 1)(x + 1) = 0 ln((1 + -1x) + x(-1 + x)) + ln(x + -1)(x + 1) + ln(x + 1)(x + 1) = 0 ln(1 + -1x + (-1 * x + x * x)) + ln(x + -1)(x + 1) + ln(x + 1)(x + 1) = 0 ln(1 + -1x + (-1x + x2)) + ln(x + -1)(x + 1) + ln(x + 1)(x + 1) = 0 Combine like terms: -1x + -1x = -2x ln(1 + -2x + x2) + ln(x + -1)(x + 1) + ln(x + 1)(x + 1) = 0 (1 * ln + -2x * ln + x2 * ln) + ln(x + -1)(x + 1) + ln(x + 1)(x + 1) = 0 (1ln + -2lnx + lnx2) + ln(x + -1)(x + 1) + ln(x + 1)(x + 1) = 0 Reorder the terms: 1ln + -2lnx + lnx2 + ln(-1 + x)(x + 1) + ln(x + 1)(x + 1) = 0 Reorder the terms: 1ln + -2lnx + lnx2 + ln(-1 + x)(1 + x) + ln(x + 1)(x + 1) = 0 Multiply (-1 + x) * (1 + x) 1ln + -2lnx + lnx2 + ln(-1(1 + x) + x(1 + x)) + ln(x + 1)(x + 1) = 0 1ln + -2lnx + lnx2 + ln((1 * -1 + x * -1) + x(1 + x)) + ln(x + 1)(x + 1) = 0 1ln + -2lnx + lnx2 + ln((-1 + -1x) + x(1 + x)) + ln(x + 1)(x + 1) = 0 1ln + -2lnx + lnx2 + ln(-1 + -1x + (1 * x + x * x)) + ln(x + 1)(x + 1) = 0 1ln + -2lnx + lnx2 + ln(-1 + -1x + (1x + x2)) + ln(x + 1)(x + 1) = 0 Combine like terms: -1x + 1x = 0 1ln + -2lnx + lnx2 + ln(-1 + 0 + x2) + ln(x + 1)(x + 1) = 0 1ln + -2lnx + lnx2 + ln(-1 + x2) + ln(x + 1)(x + 1) = 0 1ln + -2lnx + lnx2 + (-1 * ln + x2 * ln) + ln(x + 1)(x + 1) = 0 1ln + -2lnx + lnx2 + (-1ln + lnx2) + ln(x + 1)(x + 1) = 0 Reorder the terms: 1ln + -2lnx + lnx2 + -1ln + lnx2 + ln(1 + x)(x + 1) = 0 Reorder the terms: 1ln + -2lnx + lnx2 + -1ln + lnx2 + ln(1 + x)(1 + x) = 0 Multiply (1 + x) * (1 + x) 1ln + -2lnx + lnx2 + -1ln + lnx2 + ln(1(1 + x) + x(1 + x)) = 0 1ln + -2lnx + lnx2 + -1ln + lnx2 + ln((1 * 1 + x * 1) + x(1 + x)) = 0 1ln + -2lnx + lnx2 + -1ln + lnx2 + ln((1 + 1x) + x(1 + x)) = 0 1ln + -2lnx + lnx2 + -1ln + lnx2 + ln(1 + 1x + (1 * x + x * x)) = 0 1ln + -2lnx + lnx2 + -1ln + lnx2 + ln(1 + 1x + (1x + x2)) = 0 Combine like terms: 1x + 1x = 2x 1ln + -2lnx + lnx2 + -1ln + lnx2 + ln(1 + 2x + x2) = 0 1ln + -2lnx + lnx2 + -1ln + lnx2 + (1 * ln + 2x * ln + x2 * ln) = 0 1ln + -2lnx + lnx2 + -1ln + lnx2 + (1ln + 2lnx + lnx2) = 0 Reorder the terms: 1ln + -1ln + 1ln + -2lnx + 2lnx + lnx2 + lnx2 + lnx2 = 0 Combine like terms: 1ln + -1ln = 0 0 + 1ln + -2lnx + 2lnx + lnx2 + lnx2 + lnx2 = 0 1ln + -2lnx + 2lnx + lnx2 + lnx2 + lnx2 = 0 Combine like terms: -2lnx + 2lnx = 0 1ln + 0 + lnx2 + lnx2 + lnx2 = 0 1ln + lnx2 + lnx2 + lnx2 = 0 Combine like terms: lnx2 + lnx2 = 2lnx2 1ln + 2lnx2 + lnx2 = 0 Combine like terms: 2lnx2 + lnx2 = 3lnx2 1ln + 3lnx2 = 0 Solving 1ln + 3lnx2 = 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), 'ln'. ln(1 + 3x2) = 0Subproblem 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 + 3x2)' equal to zero and attempt to solve: Simplifying 1 + 3x2 = 0 Solving 1 + 3x2 = 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 + 3x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x2 = 0 + -1 3x2 = 0 + -1 Combine like terms: 0 + -1 = -1 3x2 = -1 Add '-3x2' to each side of the equation. 3x2 + -3x2 = -1 + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 = -1 + -3x2 Simplifying 0 = -1 + -3x2 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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