x-[(1/1-x)+(x^3-3x+1/x^2-1)/(a-x^2)]
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=x-[-1/(x-1)+(x³-3x+1)/(x+1)(x-1)]/[-(x²-4)]
=x+[(-x-1+x³-3x+1)/(x+1)(x-1)]/(x²-4)
=x+[(x³-4x)/(x+1)(x-1)]/(x²-4)
=x+[x(x²-4)/(x+1)(x-1)]/(x²-4)
=x+x/(x+1)(x-1)
=(x³-x+x)/(x+1)(x-1)
=x³/(x²-1)
=x+[(-x-1+x³-3x+1)/(x+1)(x-1)]/(x²-4)
=x+[(x³-4x)/(x+1)(x-1)]/(x²-4)
=x+[x(x²-4)/(x+1)(x-1)]/(x²-4)
=x+x/(x+1)(x-1)
=(x³-x+x)/(x+1)(x-1)
=x³/(x²-1)
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