[tex] \frac{x^{2}-2}{x^{2}+x} - \frac{1}{x+1}= \frac{2x-3}{x} \rightarrow \frac{x^{2}-2}{x(x+1)}- \frac{x}{x(x+1)}= \frac{2x-3}{x} \rightarrow \frac{x^{2}-x-2}{x(x+1)}= \frac{2x-3}{x} \rightarrow \\
\frac{x^{2}-2x+x-2}{x+1}= 2x-3 \rightarrow x(x-2)-1(x-2)= (x+1)(2x-3) \rightarrow \\ \\
x^{2}-x-2=2x^{2}-3x+2x-3 \rightarrow 2x^{2}-x^{2}-x+x-3+2=0 \rightarrow \\ \\
(x^{2}-1)=0 \rightarrow x= -1, x=1 \\ \\
S= 1\\ [/tex]
daca x= -1 atunci numitorul devine 0, iar fractia nu are sens. deci singura solutie e +1.
