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Simplifying x * y(1 + y2) * dx + -1(1 + x2) * dy = 0 Reorder the terms for easier multiplication: x * y * dx(1 + y2) + -1(1 + x2) * dy = 0 Multiply x * y xy * dx(1 + y2) + -1(1 + x2) * dy = 0 Multiply xy * dx dx2y(1 + y2) + -1(1 + x2) * dy = 0 (1 * dx2y + y2 * dx2y) + -1(1 + x2) * dy = 0 (1dx2y + dx2y3) + -1(1 + x2) * dy = 0 Reorder the terms for easier multiplication: 1dx2y + dx2y3 + -1dy(1 + x2) = 0 1dx2y + dx2y3 + (1 * -1dy + x2 * -1dy) = 0 Reorder the terms: 1dx2y + dx2y3 + (-1dx2y + -1dy) = 0 1dx2y + dx2y3 + (-1dx2y + -1dy) = 0 Reorder the terms: 1dx2y + -1dx2y + dx2y3 + -1dy = 0 Combine like terms: 1dx2y + -1dx2y = 0 0 + dx2y3 + -1dy = 0 dx2y3 + -1dy = 0 Solving dx2y3 + -1dy = 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(x2y2 + -1) = 0 Factor a difference between two squares. dy((xy + 1)(xy + -1)) = 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 + 1)' equal to zero and attempt to solve: Simplifying xy + 1 = 0 Reorder the terms: 1 + xy = 0 Solving 1 + xy = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + xy = 0 + -1 Combine like terms: 1 + -1 = 0 0 + xy = 0 + -1 xy = 0 + -1 Combine like terms: 0 + -1 = -1 xy = -1 Add '-1xy' to each side of the equation. xy + -1xy = -1 + -1xy Combine like terms: xy + -1xy = 0 0 = -1 + -1xy Simplifying 0 = -1 + -1xy 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 '(xy + -1)' equal to zero and attempt to solve: Simplifying xy + -1 = 0 Reorder the terms: -1 + xy = 0 Solving -1 + xy = 0 Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + xy = 0 + 1 Combine like terms: -1 + 1 = 0 0 + xy = 0 + 1 xy = 0 + 1 Combine like terms: 0 + 1 = 1 xy = 1 Add '-1xy' to each side of the equation. xy + -1xy = 1 + -1xy Combine like terms: xy + -1xy = 0 0 = 1 + -1xy Simplifying 0 = 1 + -1xy 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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