We need to solve problem 15, which is a division problem: $(a^2b - ab^2 + a^2b^2) / (-ab)$.

AlgebraPolynomial DivisionAlgebraic ManipulationExpressions
2025/4/21

1. Problem Description

We need to solve problem 15, which is a division problem: (a2bab2+a2b2)/(ab)(a^2b - ab^2 + a^2b^2) / (-ab).

2. Solution Steps

To solve this problem, we will divide each term of the polynomial by ab-ab.
(a2bab2+a2b2)/(ab)=a2babab2ab+a2b2ab(a^2b - ab^2 + a^2b^2) / (-ab) = \frac{a^2b}{-ab} - \frac{ab^2}{ab} + \frac{a^2b^2}{-ab}.
Dividing each term:
a2bab=a\frac{a^2b}{-ab} = -a
ab2ab=b\frac{-ab^2}{-ab} = b
a2b2ab=ab\frac{a^2b^2}{-ab} = -ab
So, the final expression is:
a+bab-a + b - ab

3. Final Answer

a+bab-a + b - ab

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