[dean l]

I have a problem that I cant seem to solve, wonder if you could help. The likelihood (data) follows the normal distribution y(m) ~ N[ x(1) , s^2 / m(1) ]
The prior distribution also follows the normal distribution x(1) ~ N[ x(2) , s^2 / m(2) ]

Ive been told the posterior is x(1) | y(m) ~ N [ (m(2).x(2) + m(1).y(m))/(m(2) + m(1)) , s^2 / (m(1) + m(2)) ]

I know that posterior is proportional to likelihoodxprior but not sure how to get there algebraically.