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Simplifying xy(1 + x) * dy + -1(1 + y) * dy = 0 Reorder the terms for easier multiplication: xy * dy(1 + x) + -1(1 + y) * dy = 0 Multiply xy * dy dxy2(1 + x) + -1(1 + y) * dy = 0 (1 * dxy2 + x * dxy2) + -1(1 + y) * dy = 0 (1dxy2 + dx2y2) + -1(1 + y) * dy = 0 Reorder the terms for easier multiplication: 1dxy2 + dx2y2 + -1dy(1 + y) = 0 1dxy2 + dx2y2 + (1 * -1dy + y * -1dy) = 0 1dxy2 + dx2y2 + (-1dy + -1dy2) = 0 Solving 1dxy2 + dx2y2 + -1dy + -1dy2 = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'dy'. dy(xy + x2y + -1 + -1y) = 0Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 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 '(xy + x2y + -1 + -1y)' equal to zero and attempt to solve: Simplifying xy + x2y + -1 + -1y = 0 Reorder the terms: -1 + xy + x2y + -1y = 0 Solving -1 + xy + x2y + -1y = 0 Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + xy + x2y + 1 + -1y = 0 + 1 Reorder the terms: -1 + 1 + xy + x2y + -1y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + xy + x2y + -1y = 0 + 1 xy + x2y + -1y = 0 + 1 Combine like terms: 0 + 1 = 1 xy + x2y + -1y = 1 Add '-1xy' to each side of the equation. xy + x2y + -1xy + -1y = 1 + -1xy Reorder the terms: xy + -1xy + x2y + -1y = 1 + -1xy Combine like terms: xy + -1xy = 0 0 + x2y + -1y = 1 + -1xy x2y + -1y = 1 + -1xy Add '-1x2y' to each side of the equation. x2y + -1x2y + -1y = 1 + -1xy + -1x2y Combine like terms: x2y + -1x2y = 0 0 + -1y = 1 + -1xy + -1x2y -1y = 1 + -1xy + -1x2y Add 'y' to each side of the equation. -1y + y = 1 + -1xy + -1x2y + y Combine like terms: -1y + y = 0 0 = 1 + -1xy + -1x2y + y Simplifying 0 = 1 + -1xy + -1x2y + y 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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