(1)使分式2x²-4x+2/(x-1)³的值为整数的整数x的值有多少个?因为2x²-4x+2/(x-1)³=2(x²-2x+1)/(x-1)³=2(x-1)²/(x-1)³=2/x-1又因为分式的值x的值均为整数,所以2能被(x-1)
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![(1)使分式2x²-4x+2/(x-1)³的值为整数的整数x的值有多少个?因为2x²-4x+2/(x-1)³=2(x²-2x+1)/(x-1)³=2(x-1)²/(x-1)³=2/x-1又因为分式的值x的值均为整数,所以2能被(x-1)](/uploads/image/z/2611087-7-7.jpg?t=%EF%BC%881%EF%BC%89%E4%BD%BF%E5%88%86%E5%BC%8F2x%26sup2%3B-4x%2B2%2F%28x-1%29%26sup3%3B%E7%9A%84%E5%80%BC%E4%B8%BA%E6%95%B4%E6%95%B0%E7%9A%84%E6%95%B4%E6%95%B0x%E7%9A%84%E5%80%BC%E6%9C%89%E5%A4%9A%E5%B0%91%E4%B8%AA%3F%E5%9B%A0%E4%B8%BA2x%26sup2%3B-4x%2B2%2F%28x-1%29%26sup3%3B%3D2%EF%BC%88x%26sup2%3B-2x%2B1%EF%BC%89%2F%EF%BC%88x-1%EF%BC%89%26sup3%3B%3D2%EF%BC%88x-1%29%26sup2%3B%2F%EF%BC%88x-1%29%26sup3%3B%3D2%2Fx-1%E5%8F%88%E5%9B%A0%E4%B8%BA%E5%88%86%E5%BC%8F%E7%9A%84%E5%80%BCx%E7%9A%84%E5%80%BC%E5%9D%87%E4%B8%BA%E6%95%B4%E6%95%B0%2C%E6%89%80%E4%BB%A52%E8%83%BD%E8%A2%AB%EF%BC%88x-1%EF%BC%89)
(1)使分式2x²-4x+2/(x-1)³的值为整数的整数x的值有多少个?因为2x²-4x+2/(x-1)³=2(x²-2x+1)/(x-1)³=2(x-1)²/(x-1)³=2/x-1又因为分式的值x的值均为整数,所以2能被(x-1)
(1)使分式2x²-4x+2/(x-1)³的值为整数的整数x的值有多少个?
因为2x²-4x+2/(x-1)³=2(x²-2x+1)/(x-1)³=2(x-1)²/(x-1)³=2/x-1
又因为分式的值x的值均为整数,所以2能被(x-1)整除,当x=1时,x-1=0,即分母为零,分式无意义,所以(x-1)可取的值为-2,-1,1,2,相应的x的值为0,-1,3,2,那么满足条件的x值共有4个
回答下列问题
①本题的思路是__________.
②请运用这种解题思路,求出使分式6x²-12x+6/x³-3x²+3x-1的值为整数的整数x的值有__________个.
(2)若分式m+2/m-2的值是整数,试求m的整数值.
(1)使分式2x²-4x+2/(x-1)³的值为整数的整数x的值有多少个?因为2x²-4x+2/(x-1)³=2(x²-2x+1)/(x-1)³=2(x-1)²/(x-1)³=2/x-1又因为分式的值x的值均为整数,所以2能被(x-1)
本题的思路是__________.先化简,再穷举法求值
化为6/(x-1) [x-1]={1,2,3,6},x共有8个值
m+2/m-2=k,k是整数
m+2=k(m-2) m=(2k+2)/(k-1)=2+4/(k+1)
[(k+1)]={1,2,4}m={6,-2,0,4,3,-1}