Question

已知x+3/x+2=1/(√3+√2+1),则代数式(x-3/3x-6)/((5/x-2)-x-2)的值为多少

要求写详细过程
先谢谢各位了！

Answer 1

(x+3)/(x+2)=1/(√3+√2+1)
(x+2)/(x+3)=√3+√2+1
(x+3-1)/(x+3)=√3+√2+1
(x+3)/(x+3)-1/(x+3)=√3+√2+1
1-1/(x+3)=√3+√2+1
-1/(x+3)=√3+√2

[(x-3)/(3x-6)]/[5/(x-2)-x-2]
=[(x-3)/(3x-6)]/[5/(x-2)-(x+2)(x-2)/(x-2)]
=[(x-3)/3(x-2)]/[(5-x^2+4)/(x-2)]
=[(x-3)/3]/(9-x^2)
=[(x-3)/3]/(3-x)(3+x)
=-1/[3(3+x)]
=1/3*[-1/(x+3)]
=1/3*(√3+√2)
=(√3+√2)/3