Question

question 3
0/1 pt 3 99 details
simplify the rational expression.
$\frac{3b^{2}-8b-16}{3b^{2}+16b+16}=$
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question 4
0/1 pt 3 99 details
simplify the rational expression.
$\frac{b^{2}-2b-8}{3b^{2}+b-10}cdot\frac{3b^{2}-8b+5}{b^{2}-16}=$
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Explanation:

Question 3

Step1: Factor numerator

$3b^2 - 8b - 16 = (3b + 4)(b - 4)$

Step2: Factor denominator

$3b^2 + 16b + 16 = (3b + 4)(b + 4)$

Step3: Cancel common factors

$\frac{(3b + 4)(b - 4)}{(3b + 4)(b + 4)} = \frac{b - 4}{b + 4}$

Question 4

Step1: Factor all numerators/denominators

$b^2 - 2b - 8 = (b - 4)(b + 2)$
$3b^2 + b - 10 = (3b - 5)(b + 2)$
$3b^2 - 8b + 5 = (3b - 5)(b - 1)$
$b^2 - 16 = (b - 4)(b + 4)$

Step2: Rewrite expression with factors

$\frac{(b - 4)(b + 2)}{(3b - 5)(b + 2)} \cdot \frac{(3b - 5)(b - 1)}{(b - 4)(b + 4)}$

Step3: Cancel common factors

$\frac{\cancel{(b - 4)}\cancel{(b + 2)}}{\cancel{(3b - 5)}\cancel{(b + 2)}} \cdot \frac{\cancel{(3b - 5)}(b - 1)}{\cancel{(b - 4)}(b + 4)} = \frac{b - 1}{b + 4}$

Answer:

Question 3: $\boldsymbol{\frac{b - 4}{b + 4}}$
Question 4: $\boldsymbol{\frac{b - 1}{b + 4}}$