Solve the equation [x/(x+1)]^2 + [(x+1)/x]^2 = 17/4

We'll notice that the product of the 2 ratios
x/(x+1)*(x+1)/x = 1.

If we'll square raise the product,
we'll obtain:

[x/(x+1)]^2*[(x+1)/x]^2 =
1

We'll substitute the ratio [x/(x+1)]^2 =
t

t = 1/[(x+1)/x]^2

We'll
re-write the equation:

t + 1/t =
17/4

4t^2 + 4 = 17t

We'll
subtract 17 t both sides:

4t^2 - 17t + 4 =
0

We'll apply the quadratic
formula:

t1 = [17 + sqrt(289 -
64)]/8

t1 = (17+15)/8

t1 =
32/8

t1 = 4

t2 =
(17-15)/8

t2 = 2/8

t2 =
1/4

Since t =  [x/(x+1)]^2, both values for t have to be
positive and they are.

 [x/(x+1)]^2 =
4

x/(x+1) = 2

x = 2x +
2

-x = 2

x =
-2

x/(x+1) =
-2

x = -2x - 2

3x =
-2

x =
-2/3

x/(x+1) =
1/2

2x = x+1

x =
1

x/(x+1) =
-1/2

2x = -x-1

3x =
-1

x =
-1/3

The roots of the equation
are: {-2 , -2/3 , -1/3 , 1}.