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Simplifying (x + 1) * ln(x) + -1x * ln(x + 1) = 0 Reorder the terms: (1 + x) * ln(x) + -1x * ln(x + 1) = 0 Reorder the terms for easier multiplication: ln * x(1 + x) + -1x * ln(x + 1) = 0 Multiply ln * x lnx(1 + x) + -1x * ln(x + 1) = 0 (1 * lnx + x * lnx) + -1x * ln(x + 1) = 0 (1lnx + lnx2) + -1x * ln(x + 1) = 0 Reorder the terms: 1lnx + lnx2 + -1x * ln(1 + x) = 0 Multiply x * ln 1lnx + lnx2 + -1lnx(1 + x) = 0 1lnx + lnx2 + (1 * -1lnx + x * -1lnx) = 0 1lnx + lnx2 + (-1lnx + -1lnx2) = 0 Reorder the terms: 1lnx + -1lnx + lnx2 + -1lnx2 = 0 Combine like terms: 1lnx + -1lnx = 0 0 + lnx2 + -1lnx2 = 0 lnx2 + -1lnx2 = 0 Combine like terms: lnx2 + -1lnx2 = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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