Pregunta
Rationalize the denominator of \( \frac{5}{\sqrt{9 x}} \). Assume that all variables represent positive real numbers. \( \frac{5}{\sqrt{9 x}}=\square \) (Type an exact answer, using radicals as needed.)
Ask by Warner Valdez. in the United States
Mar 14,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\[
\frac{5\sqrt{x}}{3x}
\]
Solución
We start with the expression
\[
\frac{5}{\sqrt{9x}}.
\]
1. Recognize that \(\sqrt{9x} = \sqrt{9}\sqrt{x} = 3\sqrt{x}\). So, the expression becomes
\[
\frac{5}{3\sqrt{x}}.
\]
2. To rationalize the denominator, multiply the numerator and denominator by \(\sqrt{x}\):
\[
\frac{5}{3\sqrt{x}} \times \frac{\sqrt{x}}{\sqrt{x}} = \frac{5\sqrt{x}}{3x}.
\]
Thus, the answer is
\[
\frac{5\sqrt{x}}{3x}.
\]
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Simplifique esta solución Beyond the Answer
To rationalize the denominator of \( \frac{5}{\sqrt{9 x}} \), we can multiply both the numerator and the denominator by \( \sqrt{9 x} \): \[ \frac{5}{\sqrt{9 x}} \cdot \frac{\sqrt{9 x}}{\sqrt{9 x}} = \frac{5 \cdot \sqrt{9 x}}{9 x} \] Now simplify the numerator: \[ 5 \cdot \sqrt{9 x} = 5 \cdot 3 \cdot \sqrt{x} = 15 \sqrt{x} \] Putting it all together gives us: \[ \frac{15 \sqrt{x}}{9 x} \] This simplifies to: \[ \frac{5 \sqrt{x}}{3 x} \] Thus, the final answer is: \[ \frac{5 \sqrt{x}}{3 x} \]
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