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Answer
The simplified form of the expression is \( \frac{3^{x}+1}{8 \times 3^{x}} \).
Solution
Calculate or simplify the expression \( (3^(x+1)+3)/(8*3^(x+1)) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(3^{x+1}+3\right)}{\left(8\times 3^{x+1}\right)}\)
- step1: Remove the parentheses:
\(\frac{3^{x+1}+3}{8\times 3^{x+1}}\)
- step2: Factor the expression:
\(\frac{3\left(3^{x}+1\right)}{8\times 3^{1+x}}\)
- step3: Reduce the fraction:
\(\frac{3^{x}+1}{8\times 3^{x}}\)
The simplified form of the expression \( \frac{3^{x+1}+3}{8 \cdot 3^{x+1}} \) is \( \frac{3^{x}+1}{8 \times 3^{x}} \).
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Simplify this solution Bonus Knowledge
Hey there, let’s dive into some math fun! First up, this expression can be simplified. Notice that the numerator can be factored as \( 3(3^x + 1) \). So we rewrite it: \[ \frac{3(3^x + 1)}{8 \cdot 3^{x+1}} = \frac{3(3^x + 1)}{8 \cdot 3 \cdot 3^x} = \frac{3^x + 1}{8 \cdot 3^x} \] Next, to make sense of this, let's think about what happens as \( x \) changes. As \( x \) increases, \( 3^x \) grows rapidly, making the fraction tend toward zero, meaning it practically shrinks! So, what you’re really seeing is a lovely inverse relationship with exponential growth. Keep those numbers flying and have fun exploring further!
