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Simplifying yr + (x + y) * s + xt = 0 Reorder the terms for easier multiplication: ry + s(x + y) + xt = 0 ry + (x * s + y * s) + xt = 0 ry + (sx + sy) + xt = 0 Solving ry + sx + sy + tx = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1sx' to each side of the equation. ry + sx + sy + -1sx + tx = 0 + -1sx Reorder the terms: ry + sx + -1sx + sy + tx = 0 + -1sx Combine like terms: sx + -1sx = 0 ry + 0 + sy + tx = 0 + -1sx ry + sy + tx = 0 + -1sx Remove the zero: ry + sy + tx = -1sx Add '-1sy' to each side of the equation. ry + sy + -1sy + tx = -1sx + -1sy Combine like terms: sy + -1sy = 0 ry + 0 + tx = -1sx + -1sy ry + tx = -1sx + -1sy Add '-1tx' to each side of the equation. ry + tx + -1tx = -1sx + -1sy + -1tx Combine like terms: tx + -1tx = 0 ry + 0 = -1sx + -1sy + -1tx ry = -1sx + -1sy + -1tx Divide each side by 'y'. r = -1sxy-1 + -1s + -1txy-1 Simplifying r = -1sxy-1 + -1s + -1txy-1 Reorder the terms: r = -1s + -1sxy-1 + -1txy-1
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