Question

计算题：约分、通分

1.[1+1/(x-1)]/[1+1/(x^2-1)

Answer 1

[1+1/(x-1)]/[1+1/(x^2-1)
=.[(x-1)/(x-1)+1/(x-1)]/[(x^2-1)/(x^2-1)+1/(x^2-1)
=[(x-1+1)/(x-1)]/[(x^2-1+1)/(x^2-1)]
=[x/(x-1)]/[x^2/(x^2-1)]
=[x/(x-1)]*[(x+1)(x-1)/x^2]
=(x+1)/x

Answer 2

分子分母同时乘以﹙x²-1﹚ 变为﹙x²+x﹚/x²
因为x≠0,所以再约去x。结果为﹙x+1﹚/x 或1+1/x

追问

谢了