Prooving Elastic Collisions equations

[Lord Dark]

Homework Statement

hi everyone ,, how are you all ? ,, i have these two equations and i don't know how to get them :
v1f=((m1-m2)/(m1+m2))*v1i +(2m2/(m1+m2))*v2i
V2f=((2m1/m1+m2))*v1i+((m2-m1)/(m1+m2))*v2i

Homework Equations

m1v1i+m2v2i=m1v1f+m2v2f (conservation of momentum)
0.5m1v1^2i+0.5m2v2i^2=0.5m1v1f^2+0.5m2v2f^2 (conservation of Kinetic Energy)

The Attempt at a Solution

the book reach to taking m1 & m2 as common factor then says divide the kinetic by the momentum then I'll get the results above, but when i divide i get :
v2f=v1i+v1f ,, so someone help me to get the results above because i don't like memorizing and i know that I'll forget in the exam -_-

 

[rl.bhat]

m1v1i+m2v2i=m1v1f+m2v2f (conservation of momentum)
0.5m1v1^2i+0.5m2v2i^2=0.5m1v1f^2+0.5m2v2f^2 (conservation of Kinetic Energy)
In both the equations collect the terms containing m1 on one side and m2 on other side. Then divide left hand side and right hand side and equate. You will get relation between v1i, v1f ,v2i and v2f. Using this you can find the required result.