Multiply each term (both sides) by (1+z)^2 You should get a quadratic equation (which in this case factorizes)
Let A and B be the 2 terms on the right hand side
So 100 = A+B Multiplying each term by (i+z)^2 we get 100(1+z)^2= A(1+z)^2 + B(1+z)^2
Now put back into this line what A and B stood for and you will see that some cancelling can be done.