(X^3+2X^2-X+1)/(X^2+3X-4)=
[先凑成X(X^2+3X-4)的形式,即先将(X^3+3X^2-4X)凑齐.相差的就在后面补足,多余的就留在后面,继续凑.]
=[(X^3+3X^2-4X)-(X^2+3X-4)+(6X-3)]/(X^2+3X-4)
[接着将式子拆开,分成几个分式.]
=X(X^2+3X-4)/(X^2+3X-4)-(X^2+3X-4)/(X^2+3X-4)+(6X-3)/(X^2+3X-4)
[约分.]
=X-1+(6X-3)/(X-1)(X+4)
[继续凑.]
=X-1+[(5X-5)+(X+4)-2]/(X-1)(X+4)
[分成分式相加.]
=X-1+(5X-5)/(X-1)(X+4)+(X+4)/(X-1)(X+4)-2/(X-1)(X+4)
[约分.]
=X-1+5/(X+4)+1/(X-1)-2/(X-1)(X+4)