Rut gon phan thuc a^2/(a+b)(1-b)-b^2/(a+b)(1+a)-a^2b^2/(1+a)(1-b)

To simplify the expression, let's first find a common denominator for all the terms:

(a+b)(1-b)(1+a)(1-b)

Now, let's simplify each term:

a^2 / (a+b)(1-b) = a^2 / (a+b - ab - b^2)
= a^2 / (a - ab + b - b^2)

b^2 / (a+b)(1+a) = b^2 / (a+b + ab + b^2)
= b^2 / (a + ab + b + b^2)

a^2b^2 / (1+a)(1-b) = a^2b^2 / (1 + a - b - ab)
= a^2b^2 / (1 - b + a - ab)

Now, let's substitute these simplified terms back into the original expression:

a^2 / (a - ab + b - b^2) - b^2 / (a + ab + b + b^2) - a^2b^2 / (1 - b + a - ab)

To combine the terms, we need to find a common denominator:

(a - ab + b - b^2)(a + ab + b + b^2)(1 - b + a - ab)

Now, let's simplify the expression further:

(a^2 - a^3b + ab - ab^2) - (b^2 - a^2b^2 + ab^2 + b^3) - (a^2b^2 - a^3b^3 + a^2b - a^3b^2)

Combining like terms:

a^2 - a^3b + ab - ab^2 - b^2 + a^2b^2 - ab^2 - b^3 - a^2b^2 + a^3b^3 - a^2b + a^3b^2

Simplifying further:

a^2 - a^3b + ab - ab^2 - b^2 + a^2b^2 - ab^2 - b^3 - a^2b^2 + a^3b^3 - a^2b + a^3b^2

Now, let's combine like terms:

a^2 - a^3b + ab - ab^2 - b^2 + a^2b^2 - ab^2 - b^3 - a^2b^2 + a^3b^3 - a^2b + a^3b^2

Finally, we can simplify the expression:

a^2 - a^3b + ab - ab^2 - b^2 + a^2b^2 - ab^2 - b^3 - a^2b^2 + a^3b^3 - a^2b + a^3b^2