(1) Ax2+1=x2−x−1+x+1x2+1\dfrac{A}{x^2+1} = x^2-x-1+\dfrac{x+1}{x^2+1}x2+1A=x2−x−1+x2+1x+1 A=(x2+1)(x2−x−1)+x+1=x4−x3−x2+x2−x−1+x+1=x4−x3A=(x^2+1)(x^2-x-1)+x+1=x^4-x^3-x^2+x^2-x-1+x+1=x^4-x^3A=(x2+1)(x2−x−1)+x+1=x4−x3−x2+x2−x−1+x+1=x4−x3 x2−x+1x2−1) x4 −x3 ‾ x4 −x2 ‾−x3 +x2 −x3 +x ‾x2 −x x2 −1 ‾−x +1\begin{array}{r} x^2-x+1 \\ x^2-1\big)\overline{\ x^4 \quad\ \ -x^3\ } \\ \underline{\ x^4 \qquad\ \ -x^2\ } \\ -x^3\quad\ +x^2 \\ \underline{\ -x^3 \qquad\ \ +x\ } \\ x^2\quad\ -x \\ \underline{\ x^2 \qquad\ \ -1\ } \\ -x\quad\ +1 \end{array}x2−x+1x2−1) x4 −x3 x4 −x2 −x3 +x2 −x3 +x x2 −x x2 −1 −x +1 x4−x3x2−1=x2−x+1+−x+1x2−1\dfrac{x^4-x^3}{x^2-1}=x^2-x+1+\dfrac{-x+1}{x^2-1}x2−1x4−x3=x2−x+1+x2−1−x+1 これから 商x2−x+1x^2-x+1x2−x+1 余り−x+1-x+1−x+1