Question

先化简再求值[[(x2+2x+1)/(x+2)]÷[(x2-1)/(x-1)]-x/(x+2)其中x=√3-2

Answer 1

原拍橘式=(x+1)²/(x+2)×(x-1)/袭镇团(x+1)(x-1)-x/(x+2)
=(x+1)/(x+2)-x/(x+2)
=1/(x+2)
当 x=√旅念3-2时
原式=1/√3=√3/3

Answer 2

原式=(x+1)²/(x+2)÷(x+1)(x-1)/闷毕闷(x-1)-x/(x+2)
=(x+1)²蚂弯/(x+2)÷(x+1)-x/(x+2)
=(x+1)/数含(x+2)-x/(x+2)
=(x+1-x)/(x+2)
=1/(x+2)
=1/(√3-2+2)
=√3/3