use factoring to find the simplified product of these rational expressions.

\\frac{x^2 - 1}{x^2 + 3x - 4} \cdot \frac{x^2 + 17x + 72}{x^2 - 64}\

\\frac{(x + 1)(x + ?)}{(x + \quad)(x - 8)}\

Question

use factoring to find the simplified product of these rational expressions.

\\frac{x^2 - 1}{x^2 + 3x - 4} \cdot \frac{x^2 + 17x + 72}{x^2 - 64}\

\\frac{(x + 1)(x + ?)}{(x + \quad)(x - 8)}\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Simplifying Rational Expressions", "Factoring Trinomials" ], "new_concepts": [], "current_concepts": [ "Simplifying Rational Expressions", "Factoring Trinomials", "Multiplying Rational Expressions" ] } ## Factor all numerators and denominators $$ \begin{aligned} x^2 - 1 &= (x - 1)(x + 1) \ x^2 + 3x - 4 &= (x + 4)(x - 1) \ x^2 + 17x + 72 &= (x + 8)(x + 9) \ x^2 - 64 &= (x - 8)(x + 8) \end{aligned} $$ ## Multiply and simplify the expressions $$ \begin{aligned} \frac{x^2 - 1}{x^2 + 3x - 4} \cdot \frac{x^2 + 17x + 72}{x^2 - 64} &= \frac{(x - 1)(x + 1)}{(x + 4)(x - 1)} \cdot \frac{(x + 8)(x + 9)}{(x - 8)(x + 8)} \ &= \frac{(x - 1)(x + 1)(x + 8)(x + 9)}{(x + 4)(x - 1)(x - 8)(x + 8)} \ &= \frac{(x + 1)(x + 9)}{(x + 4)(x - 8)} \end{aligned} $$ ## Identify the missing values $$ \frac{(x + 1)(x + [?])}{(x + [ \quad ])(x - 8)} = \frac{(x + 1)(x + 9)}{(x + 4)(x - 8)} $$ Use factoring to find the simplified product of these rational expressions. $$\frac{x^2 - 1}{x^2 + 3x - 4} \cdot \frac{x^2 + 17x + 72}{x^2 - 64}$$ The simplified product is: $$\frac{(x + 1)(x + 9)}{(x + 4)(x - 8)}$$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Simplifying Rational Expressions" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Factor all numerators and denominators

Multiply and simplify the expressions

Identify the missing values

Answer: