divide.

\\frac{x - 8}{2x + 18} \div \frac{7x - 56}{6x + 54}\

simplify your answer as much as possible.

Question

divide.

\\frac{x - 8}{2x + 18} \div \frac{7x - 56}{6x + 54}\

simplify your answer as much as possible.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Rational Expression Division", "Factoring Polynomials", "Simplifying Rational Expressions" ], "current_concepts": [ "Rational Expression Division", "Factoring Polynomials", "Simplifying Rational Expressions" ] } ## Convert division to multiplication by the reciprocal $$ \frac{x - 8}{2x + 18} \div \frac{7x - 56}{6x + 54} = \frac{x - 8}{2x + 18} \cdot \frac{6x + 54}{7x - 56} $$ ## Factor all polynomial expressions $$ \begin{aligned} 2x + 18 &= 2(x + 9) \ 6x + 54 &= 6(x + 9) \ 7x - 56 &= 7(x - 8) \end{aligned} $$ ## Substitute factored forms and simplify $$ \begin{aligned} \frac{x - 8}{2(x + 9)} \cdot \frac{6(x + 9)}{7(x - 8)} &= \frac{(x - 8) \cdot 6(x + 9)}{2(x + 9) \cdot 7(x - 8)} \ &= \frac{6}{2 \cdot 7} \ &= \frac{3}{7} \end{aligned} $$ $\frac{3}{7}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Rational Expression Division" ] }

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QUESTION IMAGE

Question

Explanation:

Convert division to multiplication by the reciprocal

Factor all polynomial expressions

Substitute factored forms and simplify

Answer: