when fully simplified, excluding restrictions, $\frac{x^2 + x}{2x^2 + 7x + 3} \times \frac{x + 3}{x^2 - 1}$ is equal to

a) $\frac{x}{(2x - 1)(x + 1)}$

b) $\frac{1}{2x + 1}$

c) $\frac{(x^2 + x)(x + 3)}{(2x^2 + 7x + 3)(x^2 - 1)}$

d) $\frac{x}{(2x + 1)(x - 1)}$

Question

when fully simplified, excluding restrictions, $\frac{x^2 + x}{2x^2 + 7x + 3} \times \frac{x + 3}{x^2 - 1}$ is equal to

a) $\frac{x}{(2x - 1)(x + 1)}$

b) $\frac{1}{2x + 1}$

c) $\frac{(x^2 + x)(x + 3)}{(2x^2 + 7x + 3)(x^2 - 1)}$

d) $\frac{x}{(2x + 1)(x - 1)}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Simplifying Rational Expressions", "Multiplying Rational Expressions" ], "new_concepts": [], "current_concepts": [ "Simplifying Rational Expressions", "Multiplying Rational Expressions", "Factoring Polynomials" ] } ## Factor the numerators and denominators Using the *Simplifying Rational Expressions* and *Multiplying Rational Expressions* knowledge points $$ \begin{aligned} x^2 + x &= x(x + 1) \ 2x^2 + 7x + 3 &= (2x + 1)(x + 3) \ x^2 - 1 &= (x - 1)(x + 1) \end{aligned} $$ ## Substitute and simplify the expression Using the *Simplifying Rational Expressions* and *Multiplying Rational Expressions* knowledge points $$ \begin{aligned} \frac{x^2+x}{2x^2+7x+3} \times \frac{x+3}{x^2-1} &= \frac{x(x+1)}{(2x+1)(x+3)} \times \frac{x+3}{(x-1)(x+1)} \ &= \frac{x(x+1)(x+3)}{(2x+1)(x+3)(x-1)(x+1)} \ &= \frac{x}{(2x+1)(x-1)} \end{aligned} $$

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

B) $\frac{1}{2x+1}$

C) $\frac{(x^2+x)(x+3)}{(2x^2+7x+3)(x^2-1)}$

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

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

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QUESTION IMAGE

Question

Explanation:

Factor the numerators and denominators

Substitute and simplify the expression

Answer: