Question

Which rational expression should be subtracted from x^2+6x+8/x^8+8 to get 3/x^2-2x+4

Answer 1

we should subtract x ^2+5/x ^2+8x +4.

let we subtract a from the equation

x ^2+6x +8/x ^2+8-a =3/x ^2-2x +4

a =x ^2+6x +8/x ^2+8-3/x^2+2x -4

=x^2+8/x ^2-3/x ^2+6x +2x +8-4

=x ^2+5/x ^2+8x +4=a.

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