question

multiply: $\frac{2x - 6}{x^2 - 8x + 15} \cdot \frac{x^2 - 25}{2x + 10}$.

provide your answer below:

Question

question

multiply: $\frac{2x - 6}{x^2 - 8x + 15} \cdot \frac{x^2 - 25}{2x + 10}$.

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": [ "Greatest Common Factor Factoring", "Factoring Trinomials", "Difference of Squares", "Multiplying Rational Expressions" ], "new_concepts": [], "current_concepts": [ "Greatest Common Factor Factoring", "Factoring Trinomials", "Difference of Squares", "Multiplying Rational Expressions" ] } ## Factor the numerators Using the *Greatest Common Factor Factoring* and *Difference of Squares* knowledge points $$ \begin{aligned} 2x - 6 &= 2(x - 3) \ x^2 - 25 &= (x - 5)(x + 5) \end{aligned} $$ ## Factor the denominators Using the *Factoring Trinomials* and *Greatest Common Factor Factoring* knowledge points $$ \begin{aligned} x^2 - 8x + 15 &= (x - 3)(x - 5) \ 2x + 10 &= 2(x + 5) \end{aligned} $$ ## Multiply and simplify the expression Using the *Multiplying Rational Expressions* knowledge point $$ \begin{aligned} \frac{2x - 6}{x^2 - 8x + 15} \cdot \frac{x^2 - 25}{2x + 10} &= \frac{2(x - 3)}{(x - 3)(x - 5)} \cdot \frac{(x - 5)(x + 5)}{2(x + 5)} \ &= \frac{2(x - 3)(x - 5)(x + 5)}{2(x - 3)(x - 5)(x + 5)} \ &= 1 \quad (x eq 3, 5, -5) \end{aligned} $$ Multiply: $\frac{2x - 6}{x^2 - 8x + 15} \cdot \frac{x^2 - 25}{2x + 10} =$ $1$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Multiplying Rational Expressions" ] }

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Question

Explanation:

Factor the numerators

Factor the denominators

Multiply and simplify the expression

Answer: