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The simplified form is \( \frac{3-2\sqrt{3}}{3} \).
Solución
Calculate or simplify the expression \( -1/(\sqrt(12)+3) \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{-1}{\left(\sqrt{12}+3\right)}\)
- step1: Remove the parentheses:
\(\frac{-1}{\sqrt{12}+3}\)
- step2: Simplify the root:
\(\frac{-1}{2\sqrt{3}+3}\)
- step3: Multiply by the Conjugate:
\(\frac{-\left(2\sqrt{3}-3\right)}{\left(2\sqrt{3}+3\right)\left(2\sqrt{3}-3\right)}\)
- step4: Multiply the numbers:
\(\frac{-\left(2\sqrt{3}-3\right)}{3}\)
- step5: Multiply the numbers:
\(\frac{-2\sqrt{3}+3}{3}\)
- step6: Calculate:
\(\frac{3-2\sqrt{3}}{3}\)
The simplified form of \( \frac{-1}{\sqrt{12}+3} \) is \( \frac{3-2\sqrt{3}}{3} \).
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Simplifique esta solución The Deep Dive
To simplify \( \frac{-1}{\sqrt{12}+3} \), we can multiply the numerator and denominator by the conjugate of the denominator, which is \( \sqrt{12}-3 \). This will help eliminate the square root in the denominator: \[ \frac{-1(\sqrt{12}-3)}{(\sqrt{12}+3)(\sqrt{12}-3)} = \frac{-\sqrt{12}+3}{12-9} = \frac{-\sqrt{12}+3}{3} \] Now, we can further simplify \( \sqrt{12} \) to \( 2\sqrt{3} \): \[ \frac{-2\sqrt{3}+3}{3} = 1 - \frac{2\sqrt{3}}{3} \] So the simplified form of \( \frac{-1}{\sqrt{12}+3} \) is \( 1 - \frac{2\sqrt{3}}{3} \). Feel free to ask for another math expression to tackle!
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