what is the difference?

$\frac{x+5}{x+2} - \frac{x+1}{x^2+2x}$

$\circ$ $\frac{x^2+4x-1}{x(x+2)}$

$\circ$ $\frac{x^2+4x+1}{x(x+2)}$

$\circ$ $\frac{4}{-1(x^2+x-2)}$

$\circ$ $\frac{x^2+6x+1}{x(x+2)}$

Question

what is the difference?

$\frac{x+5}{x+2} - \frac{x+1}{x^2+2x}$

$\circ$ $\frac{x^2+4x-1}{x(x+2)}$

$\circ$ $\frac{x^2+4x+1}{x(x+2)}$

$\circ$ $\frac{4}{-1(x^2+x-2)}$

$\circ$ $\frac{x^2+6x+1}{x(x+2)}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Rational Subtraction", "Least Common Denominator" ], "new_concepts": [], "current_concepts": [ "Rational Subtraction", "Least Common Denominator" ] } ## Find the least common denominator $$ \begin{aligned} &\text{Denominators: } x+2 \quad \text{and} \quad x^2+2x = x(x+2)\ &\text{LCD} = x(x+2) \end{aligned} $$ ## Rewrite fractions with the common denominator $$ \begin{aligned} &\frac{x+5}{x+2} \cdot \frac{x}{x} = \frac{x(x+5)}{x(x+2)} = \frac{x^2+5x}{x(x+2)}\ &\frac{x+1}{x^2+2x} = \frac{x+1}{x(x+2)} \end{aligned} $$ ## Subtract the numerators $$ \begin{aligned} &\frac{x^2+5x}{x(x+2)} - \frac{x+1}{x(x+2)} = \frac{(x^2+5x) - (x+1)}{x(x+2)}\ &= \frac{x^2+5x-x-1}{x(x+2)}\ &= \frac{x^2+4x-1}{x(x+2)} \end{aligned} $$

(A) $\frac{x^2+4x-1}{x(x+2)}$

(B) $\frac{x^2+4x+1}{x(x+2)}$

(C) $\frac{4}{-1(x^2+x-2)}$

(D) $\frac{x^2+6x+1}{x(x+2)}$

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

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QUESTION IMAGE

Question

Explanation:

Find the least common denominator

Rewrite fractions with the common denominator

Subtract the numerators

Answer: