Use implicit differentiation to find an equation of the tangent line to the curve at the given point $(2,4)$

Question

Find an equation of the tangent line to the curve at the given point $(2,4)$

$$x^2+2xy-y^2+x=6$$

I got a derivative of $\frac{-2y-1-2x}{2(y-x)}$ and a slope of $-3.25$ and $y=10.5-3.25x$ as my equation of the tangent line. However, this turned out to be incorrect and I can't figure what I've done wrong.

Answer 1

There may be a sign error. The correct implicit derivative is

$$\frac{2y+2x+1}{2(y-x)}$$

which gives in $(2,4)$ a slope of $\frac{13}{4}=+3.25$ and a tangent line

$$y=\frac{13}{4}x-\frac{5}{2}$$