Express the fraction (p+q)/(p-q) in the form m+n√2, where p=3-2√2 and q=2-√2.

To answer this question, m and n should be whole numbers instead of fractions, without any square root terms in them. To do this, we first find the numerator, p+q, and the denominator, p-q, individually.Numerator:p + q = 3 - 2√2 + 2 - √2 = 5 - 3√2Denominator:p - q = 3 - 2√2 -(2 - √2) = 3 - 2√2 - 2 + √2 = 1 -√2Putting the two together, this means that the fraction we need to calculate is (5 - 3√2)/(1 - √2). To rationalise just the denominator, (1 - √2), we multiply it by (1 + √2). When we do this, the square root terms will cancel out and we will be left with a whole number to divide the numerator by. In order to keep the value of the fraction the same, we also need to multiply the numerator, (5 - 3√2), by the same expression, (1 + √2).Numerator:(5 - 3√2) x (1 + √2) = 5 + 5√2 - 3√2 - (3√2 x √2) = 5 + 2√2 -6 = -1 + 2√2Denominator:(1 - √2) x (1 + √2) = 1 + √2 - √2 - (√2 x √2) = 1 - 2 = -1Putting the fraction back together gives us (-1 + 2√2)/(-1).Since the denominator in this case is -1, we need to divide each term in the numerator by -1. This gives us the answer in the correct format: 1 - 2√2, where m = 1 and n = 2.