simplify the rational expressions.

$\frac{x^2 - 16}{x^2 + 6x + 8}$

$\circ$ $\frac{x - 4}{x + 4}$
$\circ$ $\frac{x + 4}{x + 2}$
$\circ$ $\frac{x - 4}{x + 2}$

$\frac{x^2 - x - 6}{x^2 - 3x - 10}$

$\circ$ $\frac{x + 2}{x - 5}$
$\circ$ $\frac{x - 3}{x - 5}$
$\circ$ $\frac{x - 3}{x + 2}$

Question

simplify the rational expressions.

$\frac{x^2 - 16}{x^2 + 6x + 8}$

$\circ$ $\frac{x - 4}{x + 4}$
$\circ$ $\frac{x + 4}{x + 2}$
$\circ$ $\frac{x - 4}{x + 2}$

$\frac{x^2 - x - 6}{x^2 - 3x - 10}$

$\circ$ $\frac{x + 2}{x - 5}$
$\circ$ $\frac{x - 3}{x - 5}$
$\circ$ $\frac{x - 3}{x + 2}$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Rational Expressions", "Polynomial Factoring" ], "new_concepts": [], "current_concepts": [ "Rational Expressions", "Polynomial Factoring" ] } ## Factor and simplify the first expression Using the *Polynomial Factoring* and *Rational Expressions* knowledge points $$ \begin{aligned} \frac{x^2 - 16}{x^2 + 6x + 8} &= \frac{(x - 4)(x + 4)}{(x + 2)(x + 4)} \ &= \frac{x - 4}{x + 2} \quad (x eq -4) \end{aligned} $$ ## Factor and simplify the second expression Using the *Polynomial Factoring* and *Rational Expressions* knowledge points $$ \begin{aligned} \frac{x^2 - x - 6}{x^2 - 3x - 10} &= \frac{(x - 3)(x + 2)}{(x - 5)(x + 2)} \ &= \frac{x - 3}{x - 5} \quad (x eq -2) \end{aligned} $$ ## Question 1 (A) $\frac{x - 4}{x + 4}$

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

(C) $\frac{x - 4}{x + 2}$ ## Question 2 (A) $\frac{x + 2}{x - 5}$

(B) $\frac{x - 3}{x - 5}$

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

{ "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Rational Expressions" ] }

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QUESTION IMAGE

Question

Explanation:

Factor and simplify the first expression

Factor and simplify the second expression

Answer:

Question 1

Question 2