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Simplifying (a + 1) * ydx + (b + 1) * xdy = 0 Reorder the terms: (1 + a) * ydx + (b + 1) * xdy = 0 Reorder the terms for easier multiplication: dxy(1 + a) + (b + 1) * xdy = 0 (1 * dxy + a * dxy) + (b + 1) * xdy = 0 Reorder the terms: (adxy + 1dxy) + (b + 1) * xdy = 0 (adxy + 1dxy) + (b + 1) * xdy = 0 Reorder the terms: adxy + 1dxy + (1 + b) * xdy = 0 Reorder the terms for easier multiplication: adxy + 1dxy + dxy(1 + b) = 0 adxy + 1dxy + (1 * dxy + b * dxy) = 0 Reorder the terms: adxy + 1dxy + (bdxy + 1dxy) = 0 adxy + 1dxy + (bdxy + 1dxy) = 0 Reorder the terms: adxy + bdxy + 1dxy + 1dxy = 0 Combine like terms: 1dxy + 1dxy = 2dxy adxy + bdxy + 2dxy = 0 Solving adxy + bdxy + 2dxy = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1bdxy' to each side of the equation. adxy + bdxy + -1bdxy + 2dxy = 0 + -1bdxy Combine like terms: bdxy + -1bdxy = 0 adxy + 0 + 2dxy = 0 + -1bdxy adxy + 2dxy = 0 + -1bdxy Remove the zero: adxy + 2dxy = -1bdxy Add '-2dxy' to each side of the equation. adxy + 2dxy + -2dxy = -1bdxy + -2dxy Combine like terms: 2dxy + -2dxy = 0 adxy + 0 = -1bdxy + -2dxy adxy = -1bdxy + -2dxy Divide each side by 'dxy'. a = -1b + -2 Simplifying a = -1b + -2 Reorder the terms: a = -2 + -1b
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