Pregunta
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The simplified expression is \( \frac{4}{3} \).
Solución
To simplify the expression, start with:
(3^(x+1) + 3^(x+0)) / 3^(x+1)
Step 1: Recognize that 3^(x+0) is just 3^x, so the expression becomes:
(3^(x+1) + 3^x) / 3^(x+1)
Step 2: Write 3^(x+1) as 3*3^x:
(3*3^x + 3^x) / (3*3^x)
Step 3: Factor 3^x from the numerator:
3^x(3 + 1) / (3*3^x)
Step 4: Cancel 3^x from the numerator and denominator:
(3 + 1) / 3
Step 5: Simplify the expression:
4 / 3
Thus, the simplified expression is 4/3.
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución The Deep Dive
To simplify the given expression \( \frac{3^{x+1} + 3^{x}}{3^{x+1}} \), we can first factor out \( 3^{x} \) from the numerator: \[ 3^{x+1} + 3^{x} = 3^{x}(3 + 1) = 3^{x} \cdot 4 \] Now, substituting this back into the expression, we have: \[ \frac{3^{x} \cdot 4}{3^{x+1}} \] This can be simplified further by canceling \( 3^{x} \) in the numerator and denominator. Remember that \( 3^{x+1} = 3^{x} \cdot 3 \), so: \[ \frac{4}{3} \] Thus, the simplified form of the expression is: \[ \frac{4}{3} \]
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