先化简再求值 x-2分之3-x除以(x+2-x-2分之5)其中x=2√2

题目

先化简再求值 x-2分之3-x除以(x+2-x-2分之5)其中x=2√2

答案

原式=-[(x-3)/(x-2)]÷{[(x+2)(x-2)-5]/(x-2)]
=-[(x-3)/(x-2)]÷[(x²-9)/(x-2)]
=-(x-3)/(x+3)(x-3)
=-1/(x+3)
=-1/(3+2√2)
=-(3-2√2)/(9-8)
=2√2-3