Rationalize Denominator: Step 1: Rationalize the denominator by multiplying the numerator and the denominator by the conjugate of the denominator. Calculation: (1)/(2+sqrt3) * (2-sqrt3)/(2-sqrt3) Math error check: Apply Difference of Squares: Step 2: Apply the difference of squares formula to the denominator. Calculation: (2-sqrt3)/(4 - (sqrt3)^2) Math error check: Simplify Denominator: Step 3: Simplify the expression in the denominator. Calculation: (2-sqrt3)/(4 - 3) Math error check: Continue Simplifying: Step 4: Continue simplifying the expression. Calculation: (2-sqrt3)/1 Math error check: Final Simplification: Step 5: Final simplification. Calculation: 2-sqrt3 Math error check:

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Solve: $\frac{1}{2+\sqrt{3}}$

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Q. Solve:

\frac{1}{2+\sqrt{3}}

Rationalize Denominator: Step $1$ : Rationalize the denominator by multiplying the numerator and the denominator by the conjugate of the denominator. $\newline$ Calculation: $(\frac{1}{2+\sqrt{3}}) \times (\frac{2-\sqrt{3}}{2-\sqrt{3}})$ $\newline$ Math error check:
Apply Difference of Squares: Step $2$ : Apply the difference of squares formula to the denominator. $\newline$ Calculation: $(2-\sqrt{3})/(4 - (\sqrt{3})^2)$ $\newline$ Math error check:
Simplify Denominator: Step $3$ : Simplify the expression in the denominator. $\newline$ Calculation: $(2-\sqrt{3})/(4 - 3)$ $\newline$ Math error check:
Continue Simplifying: Step $4$ : Continue simplifying the expression. $\newline$ Calculation: $(2-\sqrt{3})/1$ $\newline$ Math error check:
Final Simplification: Step $5$ : Final simplification. $\newline$ Calculation: $2-\sqrt{3}$ $\newline$ Math error check: