Question 992286

Find all real or imaginary solutions for the following equation:

(1/x) + 1/(x-1) = (3/2)

I have really been struggling with using imaginaries and fractions. Help is greatly appreciated.
Thank you!
<pre>{{{1/x + 1/(x - 1) = 3/2}}}
2(x - 1) + 2x = 3x(x - 1) ------ Multiplying through by LCD: 2x(x - 1)
{{{2x - 1 + 2x = 3x^2 - 3x}}}
{{{4x - 1 = 3x^2 - 3x}}}
{{{3x^2 - 3x - 4x + 1 = 0}}}
{{{3x^2 - 7x + 1 = 0}}}
(3x - 1)(x - 2) = 0 ------ Factoring trinomial to determine solutions
3x - 1 = 0        OR       x - 2 = 0
{{{highlight_green(x = 1/3)}}}     OR       {{{highlight_green(x = 2)}}}
Both satisfy the original equation so both are solutions.