Equation of Line tangent to the curve

Question

Find the equation in point-slope form of the line tangent to the curve of x^2y-3y+2x=9 at point (2,5)

Answer 1

Implicit differentiation yields: dy/dx= -(2xy+2)/(x²-3)

Evaluate this at (2,5)

Then set this value equal to (y-5)/(x-2)...that is the equation of the tangent.