solve x+1/x-1+x-2/x+2=3

\frac{x + 1}{x - 1} + \frac{x - 2}{x + 2} = 3 \Rightarrow \frac{(x + 1) (x + 2) + (x - 2) (x - 1)}{(x - 1) (x + 2)} = 3 \Rightarrow (x + 1) (x + 2) + (x - 2) (x - 1) = 3 (x - 1) (x + 2) \Rightarrow x^{2} + 3 x + 2 + x^{2} - 3 x + 2 = 3 x^{2} + 3 x - 6 \Rightarrow 2 x^{2} + 4 = 3 x^{2} + 3 x - 6 \Rightarrow x^{2} + 3 x - 10 = 0 \Rightarrow x^{2} + 5 x - 2 x - 10 = 0 \Rightarrow x (x + 5) - 2 (x + 5) = 0 \Rightarrow (x + 5) (x - 2) = 0 \Rightarrow x = - 5 and x = 2

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