question

add: $\frac{1}{3c^4d^2} + \frac{2}{9c^5d^3}$.

provide your answer below:

Question

question

add: $\frac{1}{3c^4d^2} + \frac{2}{9c^5d^3}$.

provide your answer below:

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Least Common Denominator", "Equivalent Rational Expressions", "Adding Rational Expressions" ], "new_concepts": [], "current_concepts": [ "Least Common Denominator", "Equivalent Rational Expressions", "Adding Rational Expressions" ] } ## Find the least common denominator Using the *Least Common Denominator* knowledge point $$ \begin{aligned} &\text{Denominators: } 3c^4d^2 \text{ and } 9c^5d^3\ &\text{LCM of coefficients } (3, 9) = 9\ &\text{Highest power of } c = c^5\ &\text{Highest power of } d = d^3\ &\text{LCD} = 9c^5d^3 \end{aligned} $$ ## Convert to equivalent expressions Using the *Equivalent Rational Expressions* knowledge point $$ \begin{aligned} &\frac{1}{3c^4d^2} = \frac{1 \cdot 3cd}{3c^4d^2 \cdot 3cd} = \frac{3cd}{9c^5d^3}\ &\frac{2}{9c^5d^3} = \frac{2}{9c^5d^3} \end{aligned} $$ ## Add the rational expressions Using the *Adding Rational Expressions* knowledge point $$ \frac{3cd}{9c^5d^3} + \frac{2}{9c^5d^3} = \frac{3cd + 2}{9c^5d^3} $$ Add: $\frac{1}{3c^4d^2} + \frac{2}{9c^5d^3}$. Provide your answer below: $\frac{3cd+2}{9c^5d^3}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Adding Rational Expressions" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Find the least common denominator

Convert to equivalent expressions

Add the rational expressions

Answer: