把23x-11x^2/(2x-1)(9-x^2) 拆分成部分分式的和_数学解答

把23x-11x^2/(2x-1)(9-x^2) 拆分成部分分式的和

人气：127 ℃　时间：2020-01-26 00:37:53

解答

(23x-11x^2)/[(2x-1)(9-x^2)]
=(-4x^2+2x-7x^2+21x)/[(2x-1)(9-x^2)]
=(4x^2-2x+7x^2-21x)/[(2x-1)(x^2-9)]
=[2x(2x-1)+7x(x-3)]/[(2x-1)(x+3)(x-3)]
=2x/[(x+3)(x-3)]+7x/[(2x-1)(x+3)]
=1/(x+3)+1/(x-3)+1/(2x-1)+3/(x+3)
=4/(x+3)+1/(x-3)+1/(2x-1)