isoclines,,,never been very good with limits

can u cancel infinty,,,,this is probably a very stupid/petty question!!Q is find the equation of the straight line on which the gradient of the solution curve is infinite. I made the presumption that this straight line would essentially be an isocline(hopefulli im ryt) and did the follwing,, Is is more accurate using the D.e and making bottom=0???Or is my working ok?!

dy/dx=(3y-x)/(y+x)

dy/dx=m(constant)

putting constant as infinity and rearranging to f(x)

(i) y= -x(1-m)/(m-3)

(ii) y= -x(1-inf)/(inf-3) implies(i think) y= -x(inf)/(inf)

y = -x

is this okai???