This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To rationalize the expression (1)/(2+sqrt(3)), we multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of 2+sqrt(3) is 2-sqrt(3). Step 1: Multiply the fraction by 2-sqrt(3)2-sqrt(3). (1)/(2+sqrt(3)) × 2-sqrt(3)2-sqrt(3) Step 2: Perform the multiplication. The numerator becomes 1 × (2-sqrt(3)) = 2-sqrt(3). The denominator is in the form (a+b)(a-b) = a^2 - b^2, where a=2 and b=sqrt(3). (2+sqrt(3))(2-sqrt(3)) = 2^2 - (sqrt(3))^2 Step 3: Simplify the denominator. 2^2 - (sqrt(3))^2 = 4 - 3 = 1 Step 4: Write the simplified fraction. 2-sqrt(3)1 = 2-sqrt(3) The rationalized expression is 2-sqrt(3).