$$ \frac{3 x+1}{6} imes \frac{3}{3 x+1} $$ e $$ \frac{(2 x-4)(x+6)}{x+7} imes \frac{x+7}{2 x-4} $$

Question

$$ \frac{3 x+1}{6} 	imes \frac{3}{3 x+1} $$ e $$ \frac{(2 x-4)(x+6)}{x+7} 	imes \frac{x+7}{2 x-4} $$

UpStudy AI · Accepted Answer

1. Simplify 
   $$
   \frac{3x+1}{6} \times \frac{3}{3x+1}.
   $$

- Notice that the factor $$3x+1$$ appears in both the numerator and the denominator. Assuming $$3x+1 \neq 0$$, we can cancel it:
     $$
     \frac{\cancel{3x+1}}{6} \times \frac{3}{\cancel{3x+1}} = \frac{3}{6}.
     $$
   - Simplify the fraction:
     $$
     \frac{3}{6} = \frac{1}{2}.
     $$

2. Simplify 
   $$
   \frac{(2x-4)(x+6)}{x+7} \times \frac{x+7}{2x-4}.
   $$

- Notice that the factor $$2x-4$$ appears in both the numerator and the denominator. Also, the factor $$x+7$$ cancels:
     $$
     \frac{\cancel{2x-4}(x+6)}{\cancel{x+7}} \times \frac{\cancel{x+7}}{\cancel{2x-4}} = x+6.
     $$
   - Therefore, the simplified expression is:
     $$
     x+6.
     $$

**Final Answers:**

$$
\frac{3x+1}{6} \times \frac{3}{3x+1} = \frac{1}{2}, \quad \frac{(2x-4)(x+6)}{x+7} \times \frac{x+7}{2x-4} = x+6.
$$

*Note: In the first expression, we require $$3x+1 \neq 0$$, and in the second expression, we require $$2x-4 \neq 0$$ and $$x+7 \neq 0$$.*
$$ \frac{3x+1}{6} \times \frac{3}{3x+1} = \frac{1}{2}, \quad \frac{(2x-4)(x+6)}{x+7} \times \frac{x+7}{2x-4} = x+6. $$

\( \frac{3 x+1}{6} \times \frac{3}{3 x+1} \) e \( \frac{(2 x-4)(x+6)}{x+7} \times \frac{x+7}{2 x-4} \)

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