Pregunta
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Respuesta verificada por el tutor
Responder
\[
\frac{x - 1}{2^{x+1} + 9}
\]
Solución
Certainly! Let's simplify the given expression step by step.
**Given Expression:**
\[
\frac{3x - 2x - 1}{2^{x} + 2^{x} + 9}
\]
**Step 1: Simplify the Numerator**
Combine like terms in the numerator:
\[
3x - 2x - 1 = (3x - 2x) - 1 = x - 1
\]
**Step 2: Simplify the Denominator**
Combine like terms in the denominator:
\[
2^{x} + 2^{x} + 9 = 2 \cdot 2^{x} + 9
\]
Recall that \(2 \cdot 2^{x} = 2^{x+1}\). So,
\[
2 \cdot 2^{x} + 9 = 2^{x+1} + 9
\]
**Step 3: Write the Simplified Expression**
Putting it all together:
\[
\frac{x - 1}{2^{x+1} + 9}
\]
**Final Simplified Form:**
\[
\frac{x - 1}{2^{x+1} + 9}
\]
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución Mind Expander
To simplify the given expression, let's start with the numerator: \(3x - 2x - 1\) simplifies to \(x - 1\). Next, for the denominator \(2^x + 2^x + 9\), notice that \(2^x + 2^x\) is equivalent to \(2 \times 2^x\) or simply \(2^{x+1}\). So, the complete expression can be rewritten as: \[ \frac{x - 1}{2^{x+1} + 9} \] And there you have it, simplified without losing the essence of the original!
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