write in the form a + b root 3 but using conjugating in the first step so it becomes the equation in the image multiplied by the conjucate over the conjugate of the denominator

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Let's rationalize the fraction one over two minus square root three. First, we identify the original expression. The denominator is two minus square root three. To rationalize, we need to find the conjugate of the denominator, which is two plus square root three. We multiply the entire expression by the conjugate over itself. Now we multiply the numerators. One times the quantity two plus square root three equals two plus square root three. This gives us the fraction with two plus square root three in the numerator, and the product of two minus square root three times two plus square root three in the denominator. Now we simplify the denominator using the difference of squares formula. The product of two minus square root three times two plus square root three equals two squared minus square root three squared, which is four minus three, which equals one. Therefore, our expression becomes two plus square root three over one, which simplifies to two plus square root three. We have successfully rationalized the denominator. Our final answer is two plus square root three. When expressed in the required form a plus b square root three, we have a equals two and b equals one, giving us two plus one square root three. This completes the rationalization process using the conjugate method. Let's review our complete solution. We started with one over two minus square root three. We multiplied by the conjugate two plus square root three over itself. We simplified the numerator to get two plus square root three. We used the difference of squares formula to simplify the denominator to one. Our final answer is two plus one square root three, successfully expressed in the required a plus b square root three form.