multiply.

\\frac{6x + 54}{14x - 49} \cdot \frac{2x - 7}{2x + 18}\

simplify your answer as much as possible.

Question

multiply.

\\frac{6x + 54}{14x - 49} \cdot \frac{2x - 7}{2x + 18}\

simplify your answer as much as possible.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factoring Polynomials", "Simplifying Rational Expressions" ], "new_concepts": [ "Rational Expression Multiplication" ], "current_concepts": [ "Factoring Polynomials", "Simplifying Rational Expressions", "Rational Expression Multiplication" ] } ## Factor the numerators and denominators $$ \begin{aligned} 6x + 54 &= 6(x + 9) \ 14x - 49 &= 7(2x - 7) \ 2x + 18 &= 2(x + 9) \end{aligned} $$ ## Multiply and simplify the expressions $$ \begin{aligned} \frac{6(x + 9)}{7(2x - 7)} \cdot \frac{2x - 7}{2(x + 9)} &= \frac{6(x + 9)(2x - 7)}{7(2x - 7) \cdot 2(x + 9)} \ &= \frac{6}{7 \cdot 2} \ &= \frac{3}{7} \end{aligned} $$ Multiply. $$ \frac{6x+54}{14x-49} \cdot \frac{2x-7}{2x+18} $$ Simplify your answer as much as possible. $\frac{3}{7}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Rational Expression Multiplication" ] }

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QUESTION IMAGE

Question

Explanation:

Factor the numerators and denominators

Multiply and simplify the expressions

Answer: