(x^2-16/x^2+8x+16) + (x/x-4)

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(x^2-16/x^2+8x+16) + (x/x-4)
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(x^2-16/x^2+8x+16) + (x/x-4)
(x^2-16/x^2+8x+16) + (x/x-4)

(x^2-16/x^2+8x+16) + (x/x-4)
(x^2-16)/(x^2+8x+16)+ x/(x-4)
=(x-4)(x+4)/(x+4)^2+ x/(x-4)
=(x-4)/(x+4)+ x/(x-4)
=(x-4)^2/(x+4)(x-4)+ x(x+4)/(x-4)(x+4)
=[(x-4)^2+ x(x+4)]/(x-4)(x+4)
=(x^2-8x+16+x^2+4x)/(x-4)(x+4)
=(2x^2-4x+16)/(x-4)(x+4)
=2(x^2-2x+8)/(x-4)(x+4)
=2(x^2-2x+8)/(x^2-16)

=(x-4)(x+4)/(x+4)^2+ x/(x-4)
=(x-4)/(x+4)+ x/(x-4)
=(x-4)^2/(x+4)(x-4)+ x(x+4)/(x-4)(x+4)
=[(x-4)^2+ x(x+4)]/(x-4)(x+4)
=(x^2-8x+16+x^2+4x)/(x-4)(x+4)
=(2x^2-4x+16)/(x-4)(x+4)
=2(x^2-2x+8)/(x-4)(x+4)
=2(x^2-2x+8)/(x^2-16)

(x^2-16/x^2+8x+16) + (x/x-4)
=(x+4(x-4)/(x+4)^2+x/(x-4)
=(x-4)/(x+4)+x/(x-4)
=[(x-4)^2+x(x+4)]/[(x+4)(x-4)]
=(x^2-8x+4+x^2+4x)/[(x+4)(x-4)]
=(2x^2-4x+4)/(x^2-16)