Help solving equation with rational expressions?

Two problems :

x = 5/2 - (3/2)x

or

x = 5/2 - 3 / (2x)

I think you meant the second, since the first is always true, reducing to 1 = 5/2 - 3/2 by dividing both sides by x

The second one is solved this way :

Add the 3 / (2x) to both sides to get x + 3 / (2x) = 5/2

Put the first x over the common denominator of 2x to get : 2x^2 / (2x) + 3 / (2x) = 5/2

Then add the numerators to get : (2x^2 + 3) / 2x = 5/2

Multiply both sided by the 2x to get : 2x^2 + 3 = 10x / 2

Reduce the right side to get : 2x^2 + 3 = 5x

Set the quadratic to zero to get : 2x^2 - 5x + 3 = 0

This will factor to : (2x - 3)(x - 1) = 0

So x = 3/2

or x = 1