x/x+(1-x)/x-1/x

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x/x+(1-x)/x-1/x
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x/x+(1-x)/x-1/x
x/x+(1-x)/x-1/x

x/x+(1-x)/x-1/x
x/[x+(1-x)/(x-1/x)]
=x/[x+(1-x)/((x²-1)/x)]
=x/[x+x(1-x)/(x+1)(x-1)]
=x/[x-x(x-1)/(x+1)(x-1)]
=x/[x-x/(x+1)]
=x/[(x(x+1)-x)/(x+1)]
=x(x+1)/[x(x+1)-x]
=x(x+1)/(x²+x-x)
=x(x+1)/x²
=(x+1)/x

原式=x/{x+[(1-x)/(x-1/x)]}
=x/{x+[(1-x)/((x^2-1)/x)}
=x/{x+[x(1-x)/(x^2-1)]}
=x/{[x(x^2-1)+x(1-x)]/(x^2-1)}
=x(x^2-1)/[x(x^2-1)-x(x-1)]
=x(x-1)(x+1)/[x(x-1)(x+1)-x(x-1)]
=x(x-1)(x+1)/[x(x-1)(x+1-1)]
=(x+1)/x
=1+1/x