Verified answer

(x−y)/(x+y) = x³/y + 11

y(x−y) = x³(x+y) + 11y(x+y)

xy − y² = x⁴ + x³y + 11xy + 11y²

x⁴ + x³y + 10xy + 12y² = 0

4x³ + 3x²y + x³ dy/dx + 10y + 10x dy/dx + 24y dy/dx = 0

(x³ + 10x + 24y) dy/dx = −(4x³ + 3x²y + 10y)

dy/dx = −(4x³ + 3x²y + 10y) / (x³ + 10x + 24y)

At point (2,−1), dy/dx = −(32−12−10)/(8+20−24) = −10/4 = −5/2

Equation of tangent line:

y + 1 = −5/2 (x − 2)

y = −5/2 x + 4

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