select the correct answer.

which expression is equivalent to $\frac{2n}{n+4} + \frac{7}{n-1}$ if no denominator equals zero?

$\bigcirc$ $\frac{2n^2 + 5n + 28}{(n+4)(n-1)}$

$\bigcirc$ $\frac{2n^2 + 5n + 4}{(n+4)(n-1)}$

$\bigcirc$ $\frac{2n^2 + 6n + 28}{(n+4)(n-1)}$

$\bigcirc$ $\frac{2n^2 + 6n + 4}{(n+4)(n-1)}$

Question

select the correct answer.

which expression is equivalent to $\frac{2n}{n+4} + \frac{7}{n-1}$ if no denominator equals zero?

$\bigcirc$ $\frac{2n^2 + 5n + 28}{(n+4)(n-1)}$

$\bigcirc$ $\frac{2n^2 + 5n + 4}{(n+4)(n-1)}$

$\bigcirc$ $\frac{2n^2 + 6n + 28}{(n+4)(n-1)}$

$\bigcirc$ $\frac{2n^2 + 6n + 4}{(n+4)(n-1)}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Rational Expressions", "Least Common Denominator" ], "new_concepts": [], "current_concepts": [ "Rational Expressions", "Least Common Denominator", "Adding Rational Expressions" ] } ## Find the common denominator $$ \text{LCD} = (n + 4)(n - 1) $$ ## Rewrite each term with the common denominator $$ \frac{2n}{n + 4} + \frac{7}{n - 1} = \frac{2n(n - 1)}{(n + 4)(n - 1)} + \frac{7(n + 4)}{(n + 4)(n - 1)} $$ ## Expand and simplify the numerator $$ \begin{aligned} 2n(n - 1) + 7(n + 4) &= 2n^2 - 2n + 7n + 28 \ &= 2n^2 + 5n + 28 \end{aligned} $$ $$ \frac{2n^2 + 5n + 28}{(n + 4)(n - 1)} $$

(A) $\frac{2n^2 + 5n + 28}{(n + 4)(n - 1)}$

(B) $\frac{2n^2 + 5n + 4}{(n + 4)(n - 1)}$

(C) $\frac{2n^2 + 6n + 28}{(n + 4)(n - 1)}$

(D) $\frac{2n^2 + 6n + 4}{(n + 4)(n - 1)}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Rational Expressions" ] }

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QUESTION IMAGE

Question

Explanation:

Find the common denominator

Rewrite each term with the common denominator

Expand and simplify the numerator

Answer: