已知X-XY-2Y=0求2X+3XY-Y/X-2XY+5Y

x^2 - xy - 2y^2 = 0 ==> (x -2y)(x +y) = 0 ==> x = 2y or x = -y (1) x = 2y (2x^2 + 3xy - y^2) / (x^2 - 2xy + 5y^2) = [2* (2y)^2 + 3 * (2y) * y - y^2] / [(2y)^2 - 2 * (2y) * y + 5y^2] = [8y^2 + 6y^2 - y^2] / [4y^2 - 4y^2 + 5y^2] = (13y^2) / (5y^2) = 13/5 (2) x = -y (2x^2 + 3xy - y^2) / (x^2 - 2xy + 5y^2) = [2* (-y)^2 + 3 * (-y) * y - y^2] / [(-y)^2 - 2 * (-y) * y + 5y^2] = [2y^2 - 3y^2 - y^2] / [y^2 + 2y^2 + 5y^2] = (-2y^2) / (8y^2) = -1/4

X-XY-2Y=0 (X-2Y)(X+Y)=0 X=2Y 或 X=-Y 当X=2Y时 2X+3XY-Y/X-2XY+5Y=13/5 当X=-Y时 2X+3XY-Y/X-2XY+5Y=-2/8=-1/4