Answer:
x=2 and -1
Step-by-step explanation:
\( \frac{x}{x-1}+\frac{x-1}{x}=\frac{5}{2} \)
\( \frac{x^2+(x-1)^2}{(x-1)(x)}= \frac{5}{2} \)
\( \frac{2x^2-2x+1}{x^2-x}=\frac{5}{2} \)
\( 2(2x^2-2x+1)=5(x^2-x) \)
\( 4x^2-4x+2=5x^2-5x \)
\( x^2-x-2=0 \)
\( (x-2)(x+1)=0 \)
You could use latex to see it better.
