Answer to Question #273844 in Algebra for Stone

Question

solve the equation for x belongs to R x/x-1 is equal to x + 1/x-2

Answer 1

x/x-1 is equal to x + 1/x-2

$\frac{x}{x-1}=x+\frac{1}{x-2}\\ \frac{x}{x-1}=\frac{x^2-2x+1}{x-2}\\ \frac{x^2-2x+1}{x-2}-\frac{x}{x-1}=0\\ \frac{x^3-2x^2+x-x^2+2x-1-x^2+2x}{(x-2)(1-x)}=0\\ \frac{x^3-3x^2+5x-1}{(x-2)(1-x)}=0\\ x^3-3x^2+5x-1=0$

Solving the above equation by trial method, we get

$x=0.2290, 1.385,1.385$