To simplify the given expression, we need to combine like terms and find a common denominator:

Ax + by/$a-b$$x+y$ - bx - ay/$a+b$$x+y$ = Ax - bx + by/$a-b$$x+y$ - ay/$a+b$$x+y$ = $A-b$x + by/$a-b$$x+y$ - ay/$a+b$$x+y$

Finding a common denominator for the fractions, we get:

= $$(A-b)(x)(a+b)+by(a+b)-ay(a-b)$$ / $$(a-b)(a+b)(x+y)$$ = $$(Aa-Ab+bya+byb-aay+aay)$$ / $$(a-b)(a+b)(x+y)$$ = $Aa+byb-Ab$ / $$(a^2-b^2)(x+y)$$ = $a^2+b^2$ / $a^2-b^2$

Thus, the simplified expression is $a^2+b^2$ / $a^2-b^2$.