I've been trying to get out this question for a while now: ai) Show that (x,y,z) = (1,1,1) is a solution to the following system of equations: x + y + z = 3 2x + 2y + 2z = 6 3x + 3y +3z = 9 aii) Hence find the general solution of the system b) Express 2x^2 + 3/(x^2 + 1)^2 in partial fractions My attempt: Well ai) was simple and i got that part out with barely any effort. In aii), i dont even know how to start :( All i know is that the answer is supposed to be: (x,y,x) = λ(1,0,-1) + μ(0,1,-1) + (1,1,1,) Sorry i cant offer any attempt....i just really dont know where to start....any help at all will be appreciated here. With b) i used the matrix method.....but that wasnt the approach they were looking for. I was supposed to use the concept of repeated factors: 2x^2 + 3/(x^2 + 1)^2 = Ax + B/x^2 + 1 + CX + D/(x^2+1)^2 (multiply throughout by (x^2 + 1)^2) 2x^2 +3 = (Ax + B)(x^2 + 1) + Cx + D Let x=0 3 = B + D D = 3 - B Let x= 1 5 = (A + B)(2) + C + D 5 = 2A + 2B + C + D Substituting D = 3 - B 5 = 2A + 2B + C + 3 - B 2 = 2A + B + C Well this is where im stuck.....any help at all would be a life saver. Thank you in advance.