Question

Упростите выражение
$(frac{x}{x+1} + frac{x^{2}+1}{1- x^{2} } - frac{x}{x-1} ) : frac{x+ x^{2} }{(1-x )^{2} }$

Answer 1

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Answer 2

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