(x+2/x^2-2x-x-1/x^2-4x+4)÷4-x/x
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原式=[ (x+2)/(x²-2x) - (x-1)/(x²-4x+4) ] ÷ (4-x)/x
={ (x+2)/[x(x-2)] - (x-1)/(x-2)² } ▪ x/(4-x)
={ (x+2)(x-2)/[x(x-2)²] - x(x-2)/[x(x-2)²] } ▪x/(4-x)
={ (x²-4-x²+2x)/[x(x-2)²] } ▪ x/(4-x)
=2(x-2)/[x(x-2)] ▪ x/(4-x)
=2/(4-x)
={ (x+2)/[x(x-2)] - (x-1)/(x-2)² } ▪ x/(4-x)
={ (x+2)(x-2)/[x(x-2)²] - x(x-2)/[x(x-2)²] } ▪x/(4-x)
={ (x²-4-x²+2x)/[x(x-2)²] } ▪ x/(4-x)
=2(x-2)/[x(x-2)] ▪ x/(4-x)
=2/(4-x)
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