[tex]\frac{x^2}{x^2-x-2 } -\frac{1}{x^2+5x-14}-\frac{2}{x^2-8x+7} =\\\\= \frac{x^2}{(x+1)(x-2) } -\frac{1}{(x-2)(x+7) }-\frac{2}{(x-1)(x-7)} =\\\\=\frac{x^2(x-1)(x+7)(x-7) -(x+1)(x-1) (x-7)-2(x+1)(x-2)(x+7)}{ (x +1)(x-1)(x-2)(x+7)(x-7)}=\\\\=\frac{x^2(x-1)(x^2-49) -(x^2-1) (x-7)-2(x^2-x-2) (x+7)}{ (x +1)(x-1)(x-2)(x+7)(x-7)}=[/tex]
[tex]=\frac{x^2(x^3-49x-x^2+49) -(x^3-7x^2-x+7) -2(x^3+7x^2-x^2-7x-2x-14) }{ (x +1)(x-1)(x-2)(x+7)(x-7)}= \\\\= \frac{ x^5-49x^3-x^4+49x^2 - x^3 +7x^2+x-7 -2 x^3-14x^2+2x^2+14x+ 4x+28 }{ (x +1)(x-1)(x-2)(x+7)(x-7)}= \\\\= \frac{ x^5-x^4-52x^3+49x^2 +19x+21 }{ (x +1)(x-1)(x-2)(x+7)(x-7)}[/tex]