Eight mathematical fractions (1) Given 1 / X-1 / y = 5, find the value of fraction 3x + 5xy-3y / x-3xy-y (2) Given x + 1 / x = 3, find the value of fraction x ^ 2 + 1 / x ^ 2

Eight mathematical fractions (1) Given 1 / X-1 / y = 5, find the value of fraction 3x + 5xy-3y / x-3xy-y (2) Given x + 1 / x = 3, find the value of fraction x ^ 2 + 1 / x ^ 2

1) From 1 / X-1 / y = 5, (Y-X) / xy = 5, so Y-X = 5xy, that is, X-Y = - 5xy (3x + 5xy-3y) / (x-3xy-y) = [3 (X-Y) + 5xy] / [(X-Y) - 3xy] = (- 15xy + 5xy) / (- 5xy-3xy) = - 10 / (- 8) = 5 / 42), x + 1 / x = 3 square, (x + 1 / x) ^ 2 = 9, x ^ 2 + 2 + 1 / x ^ 2 = 9, so x ^ 2 + 1 / x ^ 2 = 9-2 = 7