For this problem a/a-1- a-1/a=4 .

Is the answer a=1 1/2. I solved it by multiplying a(a-1) both side as suggested by bobpursley. thanks

check it:

1.5/.5 - (.5)/1.5=4
3-1/3 does not equal 4
so, that is not the solution.

recheck. Or better yet, graph it to check. I see two solutions, on at a=.18 about, and one about X.3. Graph
x/(x-1) - (x-1)/x -4