1.
[tex] \frac{(x+1) ^{2} }{3x} * \frac{x ^{2} }{(x+1) ^{2} } - \frac{x-1}{2} = \frac{x}{3} - \frac{x-1}{2} = \frac{2x-3x+3}{6} = \frac{3-x}{6} [/tex]
2.
[tex] x^{3} * \frac{(x+1) ^{2} }{(3x+1) ^{2} } * \frac{x+1}{(x-1)(3x+1)} + \frac{1}{1-x} = \frac{x ^{3} *(x+1) ^{3} }{(3x+1) ^{3}*(x-1) } - \frac{1}{x-1} [/tex]
[tex] \frac{x ^{3}*(x+1) ^{3}-(3x+1) ^{3} }{(3x+1) ^{3} *(x-1)} [/tex]
Cred ca e ceva gresit aici...
3.
[tex]( \frac{x ^{3}-1 }{x} : \frac{x ^{2}+x+1 }{x} + \frac{1}{x+1} ): x^{2} =[ \frac{(x-1)( x^{2} +x+1)}{x} * \frac{x}{ x^{2} +x+1} + \frac{1}{x+1} ]* \frac{1}{ x^{2} } [/tex]
[tex](x-1+ \frac{1}{x+1} )* \frac{1}{ x^{2} } = \frac{x(x+1)-x-1+1}{x+1} * \frac{1}{ x^{2} } = \frac{ x^{2} +x-x}{x+1} * \frac{1}{ x^{2} } = \frac{1}{x+1} [/tex]
