+33661 $$$$\frac{-1-x^2}{(1+x*y)^2+(x-y)^2}$$\\
Expand the denominator $$(1+x*y)^2+(x-y)^2=1+2x*y+x^2*y^2+x^2-2x*y+y^2$$\\
Collect terms in the denominator
$$1+x^2+y^2+x^2*y^2 = 1+x^2+y^2*(1+x^2)=(1+x^2)*(1+y^2)$$\\
The original numerator can be written as $$-(1+x^2)$$\\
Putting the numerator and denominator together again we have
$$\frac{-(1+x^2)}{(1+x^2)*(1+y^2)}= \frac{-1}{1+y^2}$$
+33661 $$$$\frac{-1-x^2}{(1+x*y)^2+(x-y)^2}$$\\
Expand the denominator $$(1+x*y)^2+(x-y)^2=1+2x*y+x^2*y^2+x^2-2x*y+y^2$$\\
Collect terms in the denominator
$$1+x^2+y^2+x^2*y^2 = 1+x^2+y^2*(1+x^2)=(1+x^2)*(1+y^2)$$\\
The original numerator can be written as $$-(1+x^2)$$\\
Putting the numerator and denominator together again we have
$$\frac{-(1+x^2)}{(1+x^2)*(1+y^2)}= \frac{-1}{1+y^2}$$
