Question

module 2 practice test
score: 1/16 answered: 1/16
question 2
simplify the following expression completely.
\\(\frac{3x^{2}-2x - 1}{3x^{2}-11x - 4}\\)
enter the numerator and denominator separately in the box number 1. do not leave either box blank. answer:
numerator preview:
denominator preview:
question help:
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Explanation:

Step1: Factor the numerator

Factor $3x^{2}-2x - 1$. We need two numbers that multiply to $3\times(-1)=-3$ and add up to $-2$. The numbers are $-3$ and $1$. So, $3x^{2}-2x - 1=3x^{2}-3x + x - 1=3x(x - 1)+(x - 1)=(3x + 1)(x - 1)$.

Step2: Factor the denominator

Factor $3x^{2}-11x - 4$. We need two numbers that multiply to $3\times(-4)=-12$ and add up to $-11$. The numbers are $-12$ and $1$. So, $3x^{2}-11x - 4=3x^{2}-12x+x - 4=3x(x - 4)+(x - 4)=(3x + 1)(x - 4)$.

Step3: Simplify the fraction

$\frac{3x^{2}-2x - 1}{3x^{2}-11x - 4}=\frac{(3x + 1)(x - 1)}{(3x + 1)(x - 4)}$. Cancel out the common factor $(3x + 1)$ (assuming $x
eq-\frac{1}{3}$). The simplified fraction is $\frac{x - 1}{x - 4}$.

Answer:

Numerator: $x - 1$
Denominator: $x - 4$