[tex]1).\displaystyle F(x)= \frac{3-x^2}{x^2+2} \\ \\ F( \sqrt{2} )= \frac{3- \sqrt{2} ^2}{ \sqrt{2} ^2+2} = \frac{3-2}{2+2} = \frac{1}{4} \\ \\ 2). \frac{2x+1}{x} = \frac{(x-2)(2x+1)}{x(x-2)} = \frac{2x^2+x-4x-2}{x(x-2)} = \\ \\ = \frac{2x^2-3x-2}{x(x-2)} = \frac{(x-2)(2x+1)}{x(x-2)} = \frac{2x+1}{x} \\ \\ 3). \frac{x^2}{x+1} = \frac{x^2(x-1)}{(x-1)(x+1)} \\ \\ \frac{x}{x^2-1} = \frac{x}{(x-1)(x+1)} [/tex]
[tex]\displaystyle 4). \frac{x^2+x}{x+x+x} = \frac{x(x+1)}{3x} = \frac{x+1}{3} \\ \\ 5). \frac{x^2+5x+6}{x^2-9} = \frac{(x+3)(x+2)}{(x-3)(x+3)} = \frac{x+2}{x-3} \\ \\ 6). \frac{x-1}{x} - \frac{x}{x+1} = \frac{(x+1)(x-1)-x^2}{x(x+1)} = \frac{x^2-1-x^2}{x(x+1)} =- \frac{1}{x(x+1)} [/tex]
