将分式(10x^2+30x+20)/(x^3+2x^2-x-2)约分,再求使分式值为正整数时,整数x的值_数学解答

将分式(10x^2+30x+20)/(x^3+2x^2-x-2)约分,再求使分式值为正整数时,整数x的值

人气：326 ℃　时间：2020-03-18 01:41:28

解答

(10x^2+30x+20)/(x^3+2x^2-x-2)＝10(x^2+3x+2)/[x^2(x+2)-(x+2)]
=[10(x+2)(x+1)]/[(x+2)(x^2-1]
=[10(x+2)(x+1)]/[(x+2)(x-1)(x+1)]
=10/(x-1)
要使分式值为正整数时,整数x的值应为2、3、6、11