(1/x-3)-(6/x^2-9)-(x-1/6+2x)
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(1/x-3)-(6/x^2-9)-(x-1/6+2x)
=1/(x-3)-6/[(x-3)(x+3)]-(x-1)/[2(x+3)]
=[2(x+3)-12-(x-1)(x-3)]/[2(x-3)(x+3)]
=(2x+6-12-x²+4x-3)/[2(x-3)(x+3)]
=(-x²+6x-9)/[2(x-3)(x+3)]
=-(x-3)²/[2(x-3)(x+3)]
=(3-x)/[2(x+3)]
=1/(x-3)-6/[(x-3)(x+3)]-(x-1)/[2(x+3)]
=[2(x+3)-12-(x-1)(x-3)]/[2(x-3)(x+3)]
=(2x+6-12-x²+4x-3)/[2(x-3)(x+3)]
=(-x²+6x-9)/[2(x-3)(x+3)]
=-(x-3)²/[2(x-3)(x+3)]
=(3-x)/[2(x+3)]
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