examples: divide

\\frac{-x^3y - x^2y^2 - xy^4}{-x^2y^2}\

Question

examples: divide

\\frac{-x^3y - x^2y^2 - xy^4}{-x^2y^2}\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Division by Monomial", "Exponent Rules" ], "new_concepts": [], "current_concepts": [ "Polynomial Division by Monomial", "Exponent Rules" ] } ## Split the expression into separate terms $$ \frac{-x^3y - x^2y^2 - xy^4}{-x^2y^2} = \frac{-x^3y}{-x^2y^2} + \frac{-x^2y^2}{-x^2y^2} + \frac{-xy^4}{-x^2y^2} $$ ## Simplify each term using exponent rules $$ \begin{aligned} \frac{-x^3y}{-x^2y^2} &= \frac{x}{y} \ \frac{-x^2y^2}{-x^2y^2} &= 1 \ \frac{-xy^4}{-x^2y^2} &= \frac{y^2}{x} \end{aligned} $$ ## Combine the simplified terms $$ \frac{x}{y} + 1 + \frac{y^2}{x} $$ $\frac{x}{y} + 1 + \frac{y^2}{x}$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Division by Monomial" ] }

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QUESTION IMAGE

Question

Explanation:

Split the expression into separate terms

Simplify each term using exponent rules

Combine the simplified terms

Answer: