ESPRESSIONI CON LE FRAZIONI ALGEBRICHE

${(\frac{6 x}{x^{2} - 9} + \frac{x}{x + 3} + \frac{3}{3 - x})}^{3} : {(\frac{x}{x - 2} + \frac{8}{4 - x^{2}} - \frac{2}{x + 2})}^{4}$ (R)
${(\frac{x + 5}{x^{2} + 5 x + 6} + \frac{2}{x + 3} - \frac{2}{x + 2})}^{2} : \frac{x - 1}{x^{3} + 3 x^{2} - 4}$ (R)
${[(\frac{2}{x} + \frac{x}{2} + 1) : (\frac{1}{2} + x)]}^{2} : {(\frac{8 - x^{3}}{4 - x^{2}})}^{2}$ (R)
$(\frac{x + 2}{2 x - 4} + \frac{2 - x}{4 + 2 x} + \frac{8}{x^{2} - 4}) : \frac{4}{x - 2}$ (R)
$\frac{2 x + 3}{x^{3} + x^{2} + x + 1} + \frac{2 x (x + 2) + 4}{x^{4} - 1} - \frac{3 x + 2}{x^{3} - x^{2} + x - 1} - \frac{1}{x^{2} + 1}$ (R)
$\frac{2 x + 7}{x^{3} + 2 x^{2} - x - 2} - \frac{3}{x^{2} + x - 2} + \frac{2}{x^{2} + 3 x + 2} - \frac{1}{x^{2} - 1}$ (R)
$\frac{3 x}{x^{3} - x^{2} - x + 1} - \frac{3 x}{2 - 2 x^{2}} + \frac{x - 2}{4 x - 2 x^{2} - 2} - \frac{x + 1}{x^{2} + 1 - 2 x}$ (R)
$1 - \frac{x - 1}{x + 1} + \frac{2 x - x^{2} - 1}{1 + 2 x + x^{2}} + \frac{3 + 3 x + x^{2} + x^{3}}{1 + 3 x + 3 x^{2} + x^{3}}$ (R)
$[(\frac{x + 5}{x^{2} - 5 x + 6} - \frac{x - 3}{x^{2} + 3 x - 10} + \frac{x - 2}{x^{2} + 2 x - 15}) \cdot (\frac{x}{x + 10} - \frac{1}{x + 2} + \frac{2 x}{x^{2} + 12 x + 20}) + 1] \cdot (3 - \frac{x}{x - 2})$ (R)
$[{(x - \frac{x^{2}}{x + y})}^{2} : {(y + \frac{y^{2}}{x - y})}^{2}] : (\frac{x}{y} - \frac{y}{x}) : (\frac{x}{x + y} + \frac{y}{x - y}) \cdot (\frac{x + y}{x - y} + \frac{x - y}{x + y}) : {(\frac{xy}{x + y})}^{2} : \frac{xy (x + y)}{x - y}$ (R)
$\frac{x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1}{x^{4} + x} + \frac{1}{x} + \frac{x - 1}{x^{2} + 2 x + 1} - \frac{2}{x^{3} + 2 x^{2} + x} + \frac{x^{3} - 2}{4 x^{2}} - \frac{x}{4} + \frac{1}{2 x^{2}} + 1$ (R)
${(2 x + 2 y) \cdot (\frac{x^{2} - y^{2}}{x + y})}^{3} \cdot {(\frac{x^{2} - y^{2}}{x + y})}^{- 4} \cdot (1 + \frac{2 y}{x - y}) {[(1 - \frac{2 xy}{x^{2} + xy + y^{2}}) : \frac{x^{3} + y^{3}}{x^{3} - y^{3}}]}^{2}$ (R)