Question
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Answer
The simplified form of the expression is 5.
Solution
Calculate or simplify the expression \( (2^x+2^{x+2})/(2^{x+1}-2^x) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(2^{x}+2^{x+2}\right)}{\left(2^{x+1}-2^{x}\right)}\)
- step1: Remove the parentheses:
\(\frac{2^{x}+2^{x+2}}{2^{x+1}-2^{x}}\)
- step2: Add the terms:
\(\frac{5\times 2^{x}}{2^{x+1}-2^{x}}\)
- step3: Subtract the terms:
\(\frac{5\times 2^{x}}{2^{x}}\)
- step4: Rewrite the expression:
\(5\times 1\)
- step5: Multiply:
\(5\)
The simplified form of the expression \( \frac{2^{x}+2^{x+2}}{2^{x+1}-2^{x}} \) is \( 5 \).
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Simplify this solution Bonus Knowledge
Let's simplify the expression \( \frac{2^{x}+2^{x+2}}{2^{x+1}-2^{x}} \) step by step. First, simplify the numerator: \[ 2^{x} + 2^{x+2} = 2^{x} + 2^{x} \cdot 2^2 = 2^{x} + 4 \cdot 2^{x} = 5 \cdot 2^{x} \] Now, simplify the denominator: \[ 2^{x+1} - 2^{x} = 2 \cdot 2^{x} - 2^{x} = (2 - 1) \cdot 2^{x} = 1 \cdot 2^{x} = 2^{x} \] Now we can rewrite the entire expression: \[ \frac{5 \cdot 2^{x}}{2^{x}} = 5 \] So, the simplified form of the expression \( \frac{2^{x}+2^{x+2}}{2^{x+1}-2^{x}} \) is \( 5 \).
