Hey guys i'm banging my head against the wall with this question.

dy/dx = (e^(x+y) ) / y-1

i've tried multiplying top & bottom by e^-y and seperating, but I cant seem to match the answer in the back of the book which is e^x + ye^-y = C

The fact that the equation is equal to C gave me the idea that it might be exact, but when I tried the partial derivative test I couldn't get a single variable by itself (I might have screwed up there somewhere also)

Thanks in advance