need help with implicit differentiation

Question

Here is the question:

Find dy/dx using implicit differentiation.

(3x^2+8y)/(4x+5y^2)=-22

Here is the answer I got: (6*x^2 + 15*x*y^2 - 16*y)/(15*x^2*y - 16*x + 20*y^2)

I know I need to First clear the denominator to get 3x2+8y=−22(4x+5y^2)

Answer 1

(3x²+8y)/(4x+5y²)=-22; d/dx((3x²+8y)/(4x+5y²)) = 0;

(6x + 8y')(4x + 5y²) - (4 +10yy')((3x² + 8y) = 0;

y'(32x + 40y²- 30x²y - 80y²) = 12x² + 32y - 24x² - 30xy²;

y' = (16y - 6x² - 15xy²)/(16x - 20y² - 15x²y)