How do you separate out i/i+1?

if you mean i/(i+1) , the answer is;

$\sqrt{-1}/(\sqrt{-1}+1)$

now, multiply each side with $(\sqrt{-1}-1)$

you will get $(-1-\sqrt{-1})/(-1-1)$

that is $(-1-\sqrt{-1})/-2$

get rid of the ((-)) ; the answer is most basic this;

$(1+\sqrt{-1})/2$

$(1+i)/2$

if you mean (i/i)+1, that is 1+1=2 -_-

1+1=2

i/(i+1)=1/2+i/2

$\frac{i}{i+1}=\frac {i(i-1)}{(i+1)(i-1)}=\frac {-1-i}{-1-1}=\frac{1+i}{2}=\frac12+\frac 12i$

as the same as $a+bi$

God d**n it Solveit xD, i was really annoyed with your answer and i decided to answer it properly, and after 1 hour of your answer you just posted the answer really xD