add.

\\frac{4bv}{9dk^2} + \frac{u}{6bd^2}\

simplify your answer as much as possible.

Question

add.

\\frac{4bv}{9dk^2} + \frac{u}{6bd^2}\

simplify your answer as much as possible.

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 Multiple", "Simplifying Rational Expressions" ], "new_concepts": [ "Adding Rational Expressions" ], "current_concepts": [ "Least Common Multiple", "Simplifying Rational Expressions", "Adding Rational Expressions" ] } ## Find the least common denominator Using the *Least Common Multiple* knowledge point $$ \begin{aligned} &\text{Denominator 1: } 9dk^2 = 3^2 \cdot d \cdot k^2\ &\text{Denominator 2: } 6bd^2 = 2 \cdot 3 \cdot b \cdot d^2\ &\text{LCD} = \operatorname{lcm}(9, 6) \cdot \operatorname{lcm}(d, d^2) \cdot b \cdot k^2 = 18bd^2k^2 \end{aligned} $$ ## Convert fractions to the common denominator Using the *Simplifying Rational Expressions* knowledge point $$ \begin{aligned} &\frac{4bv}{9dk^2} = \frac{4bv \cdot (2bd)}{9dk^2 \cdot (2bd)} = \frac{8b^2dv}{18bd^2k^2}\ &\frac{u}{6bd^2} = \frac{u \cdot (3k^2)}{6bd^2 \cdot (3k^2)} = \frac{3k^2u}{18bd^2k^2} \end{aligned} $$ ## Add the numerators together Combine the numerators over the common denominator: $$ \frac{8b^2dv + 3k^2u}{18bd^2k^2} $$ Add. $$ \frac{4bv}{9dk^2} + \frac{u}{6bd^2} $$ Simplify your answer as much as possible. $\frac{8b^2dv + 3k^2u}{18bd^2k^2}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Adding Rational Expressions" ] }

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QUESTION IMAGE

Question

Explanation:

Find the least common denominator

Convert fractions to the common denominator

Add the numerators together

Answer: