Solve the equation for x: [(1-x)/x] + [x/(1-x)] = 17/4

To solve (1-x)/x +x/(1-x) = 17/4

We
see that (1-x)/x and x/(1-x) are recprocals. So we put x/(1-x) =
t.

Then 1/t+t = 17/4, where t =
x/(1-x)

Multiplying by 4t we
get:

4t^2+4 = 17t

Therefore 4t^2-17t +4
= 0

(4t - 1)(t-4) = 0. 4t-1 = 0 or t = 1/4
.

So t = 1/4 gives x/(1-x) = 1/4 , Or 4x = 1-x , Or 5x= 1 , x =
1/5.

t-4 = 0 gives t = 4, or  x/(1-x) = 4, x = 4-4x. So  5x= 4, or x
= 4/5.

So x= 1/5, Or x =  4/5.