Question

化简求值:(x-4/x²-1)/(x²-3x-4/x²+2x+1)+(1/x-1),其中,x=2*√3-1

谢谢各位大虾指教,要过程.

Answer 1

原式=[(x-4)/(x+1)(x-1)]*(x+1)²/[(x-4)(x+1)]+1/(x-1)
=1/(x-1)+1/(x-1)
=2/(x-1)
代入x=2√3-1
原式=2/(2√3-2)=1/(√3-1)=(√3+1)/2

Answer 2

(x-4/x²-1)/(x²-3x-4/x²+2x+1)+(1/x-1)
=(x-4)(x²+2x+1)/[(x²-1)(x²-3x-4)]+1/(x-1)
=(x-4)(x+1)²/[(x-1)(x+1)(x-4)(x+1)]+1/(x-1)
=2/(x-1)
=2/(2√3-1 -1)
=1/(√3-1)
=(√3+1)/2