write as a single fraction.

\ -\frac{8a - 6b}{3a} + \frac{5a + 4b}{6a} - 3 \

simplify your answer as much as possible.

Question

write as a single fraction.

\ -\frac{8a - 6b}{3a} + \frac{5a + 4b}{6a} - 3 \

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 Expressions", "Common Denominator" ], "current_concepts": [ "Rational Expressions", "Common Denominator" ] } ## Find a common denominator $$ \text{LCD} = 6a $$ ## Rewrite each term with the common denominator $$ \begin{aligned} -\frac{8a - 6b}{3a} &= -\frac{2(8a - 6b)}{6a} = \frac{-16a + 12b}{6a} \ \frac{5a + 4b}{6a} &= \frac{5a + 4b}{6a} \ -3 &= -\frac{18a}{6a} \end{aligned} $$ ## Combine the numerators over the common denominator $$ \begin{aligned} \frac{(-16a + 12b) + (5a + 4b) - 18a}{6a} &= \frac{-16a + 5a - 18a + 12b + 4b}{6a} \ &= \frac{-29a + 16b}{6a} \end{aligned} $$ $\frac{-29a+16b}{6a}$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Rational Expressions" ] }

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Question

Explanation:

Find a common denominator

Rewrite each term with the common denominator

Combine the numerators over the common denominator

Answer: