Question

Find derivative for `(y+x)/(y-2)- (3y)/(x^2)=0` ?

Answer 1

`y'=-(3x^2+2xy)/(x^2-6y+6)`

Explanation:

Assuming that `y=y(x)` is hold.
Multiplying the given equation by `x^2(y-2)` we get

`x^2(y+x)-3y(y-2)=0`
expanding

`x^3+x^2y-3y^2+6y=0`
Differentiating with respect to `x`

`2xy+x^2y'+3x^2-6yy'+6y'=0`

`y'(x^2-6y+6)=-3x^2-2xy`
so `y'` is given by

`y'=-(3x^2+2xy)/(x^2-6y+6)` if `x^2-6y+6ne 0`