Find all real values of x such that
(2x^2 - 3x)/(x^2 - x) + 5x - 11 = (3x^2 + 4)/(x^2 - 1)
\(\frac{2x^{2}-3x}{x^{2}-x}+5x-11=\frac{3x^{2}+4}{x^{2}-1}\) (Problem)
\(\frac{x(2x-3)}{x(x-1)}+5x-11=\frac{3x^{2}+4}{(x+1)(x-1)}\) (Factor out the x and expand \(x^{2}-1\))
\(\frac{2x-3}{x-1}+5x-11=\frac{3x^{2}+4}{(x+1)(x-1)}\) (Cancel the x)
\((2x-3)(x+1)+5x(x-1)(x+1)-11(x-1)(x+1)=3x^{2}+4\) (Multiply everything by (x-1)(x+1) to get rid of the denominator on the right hand side)
\((2x^{2}-x-3)+(5x^{3}-5x)-(11x^{2}-11)=3x^{2}+4\) (Expand)
\(5x^{3}-9x^{2}-6x+8=3x^{2}+4\) (Simplify)
\(5x^{3}-12x^{2}-6x-4=0\) (Simplify)
I hope you can take it from here!
