因式分解及分式计算1.因式分解1.x^5+x-12.(a+b)(a+b-ab)+(ab-1)(ab+1)2.已只:n为正整数,且n^$-16n^2+100为质数,求n.3.设a=x/(y+z),b=y/(x+z),c=z/(x+y),且x+y+z≠0求a/(a+1)+b/(b+1)+c/(c+1)
问题描述：
因式分解及分式计算
1.因式分解1.x^5+x-1
2.(a+b)(a+b-ab)+(ab-1)(ab+1)
2.已只:n为正整数,且n^$-16n^2+100为质数,求n.
3.设a=x/(y+z),b=y/(x+z),c=z/(x+y),且x+y+z≠0
求a/(a+1)+b/(b+1)+c/(c+1)
答
(x^2-x+1)*(x^3+x^2-1)
n
x/(y+z)/(x/(y+z)+1)+y/(x+z)/(y/(x+z)+1)+z/(x+y)/(z/(x+y)+1)
答
应该没办法分解 2.(a+b)(a+b-ab)+(ab-1)(ab+1) =(a+b)(1-ab)-(1-ab)(1+ab) =(1-ab)(a+b-ab-1) =(1-ab)(a-1)(1-b) 3.n^4-16n^2+100 =(n^2-6n+10)(n^2+6n+10) n^4-16n^2+100为质数 n^2-6n+10=1 or n^2+6n+10=1 n=3 or ...