Question

数学分式求解。

Answer 1

1、x/(x-1)² ÷(x+1+x²-1)/(x²-1)
=x/(x-1)²×(x+1)(x-1)/x(x+1)
=1/(x-1)
当x=√2+1时
原式=1/(√2+1-1)=√2/2

2、x/x(x+1)÷(x+2)(x-1)/(x+1)(x-1) +(x+1)/(x+2)
=1/(x+1)×(x+1)/(x+2)+(x+1)/(x+2)
=1/(x+2)+(x+1)/(x+2)
=1

=a(a-1)×(a-1)/(a-1)²
=a

原式=2/(a-1) +(a-2)²/(a+1)(a-1)×(a+1)/(a-2)
=2/(a-1)+(a-2)/(a-1)
=a/(a-1)
当a=1+√2时
原式=(1+√2)/(1+√2-1)
=(√2+2)/2