Question

先化简代数式 [x+1分之x-1加上x²-1分之2x]÷x²-1分之1,然后选取一个使原式有意义的x

Answer 1

原式=[(x-1)/(x+1) +2x/(x²-1)]÷1/(x²-1)

=[(x-1)/(x+1) +2x/(x²-1)]×(x²-1)

=(x²-1)×(x-1)/(x+1) +(x²-1)×2x/(x²-1)

=(x-1)²+2x

=x²-2x+1+2x

=x²+1

要使代数式有意义,分母不能等于0,x+1≠0 且 x²-1≠0；所以 x≠±1

当x=2时

原式=2²+1=4+1=5