on the curve x + xy + 2y^2 = 6 what is the slope of the line tangent to the curve at the point (2,1)

i found the derivative:

1 + x(dy/dx) +y(1) +4y(dy/dx) =0

i solved and got dy/dx = -1(y+1)/4xy

but when i put the point 2,1 in i didnt get an answer they gave you. (i got -1/4, its a multiple choice problem and its not there). what am i doing wrong?