First we expand the expression (sinx+cosx)^2:

(sin^2(x) + 2sinx*cosx + cos^2(x))

Now we divide this expression by sin(2x)+1:

(sin^2(x) + 2sinx*cosx + cos^2(x)) / (sin(2x) + 1)

We know that sin(2x) = 2sinxcosx, so we can substitute this into our expression:

(sin^2(x) + 2sinx*cosx + cos^2(x)) / (2sinxcosx + 1)

At this point, the expression can't be simplified any further.