Упростите выражение[tex] (\frac{x}{x+1} + \frac{x^{2}+1}{1- x^{2} } - \frac{x}{x-1} ) : \frac{x+ x^{2} }{(1-x )^{2} } [/tex]. Created by NastyaLittle. algebra-ru

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Упростите выражение
[tex] (\frac{x}{x+1} + \frac{x^{2}+1}{1- x^{2} } - \frac{x}{x-1} ) : \frac{x+ x^{2} }{(1-x )^{2} } [/tex]

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Yena $(\frac{x}{x+1}+\frac{x^{2}+1}{1- x^{2}}-\frac{x}{x-1}) : \frac{x+ x^{2}}{(1-x)^{2}}=\\\ = (\frac{x}{x+1}+\frac{x^{2}+1}{(1-x)(1+x)}+\frac{x}{1-x}) : \frac{x(1+x)}{(1-x)^{2}}=\\\ =\frac{x(1-x)+x^{2}+1+x(x+1)}{(1-x)(1+x)}*\frac{(1-x)^{2}}{x(1+x)}=\\\ =\frac{x-x^2+x^{2}+1+x^2+x}{1+x}*\frac{1-x}{x(1+x)}=\frac{x^2+2x+1}{1+x}*\frac{1-x}{x(1+x)}=\\\ =\frac{(x+1)^2}{1+x}*\frac{1-x}{x(1+x)}=\frac{1-x}{x}$

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