question

add: $\frac{2}{x - 2} + \frac{5}{x + 3}$.

provide your answer below:

Question

question

add: $\frac{2}{x - 2} + \frac{5}{x + 3}$.

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": [ "Least Common Denominator", "Equivalent Rational Expressions", "Adding Rational Expressions" ], "new_concepts": [], "current_concepts": [ "Least Common Denominator", "Equivalent Rational Expressions", "Adding Rational Expressions" ] } ## Find the least common denominator Using the *Least Common Denominator* knowledge point $$ \text{LCD} = (x - 2)(x + 3) $$ ## Convert to equivalent rational expressions Using the *Equivalent Rational Expressions* knowledge point $$ \begin{aligned} \frac{2}{x - 2} &= \frac{2(x + 3)}{(x - 2)(x + 3)} \ \frac{5}{x + 3} &= \frac{5(x - 2)}{(x - 2)(x + 3)} \end{aligned} $$ ## Add the numerators Using the *Adding Rational Expressions* knowledge point $$ \begin{aligned} \frac{2(x + 3) + 5(x - 2)}{(x - 2)(x + 3)} &= \frac{2x + 6 + 5x - 10}{(x - 2)(x + 3)} \ &= \frac{7x - 4}{(x - 2)(x + 3)} \end{aligned} $$ Add: $\frac{2}{x - 2} + \frac{5}{x + 3}$. Provide your answer below: $\frac{7x - 4}{(x - 2)(x + 3)}$ { "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 to equivalent rational expressions

Add the numerators

Answer: