Question

化简求值、

先化简，再计算 （1+3/(a_2)）除以a+1/(a2_2). a=根号2－3

Answer 1

原式=[1+3/(a-2)]÷[(a+1)/(a²-2)]
={ [(a-2)+3]/(a-2) }×[(a²-2)/(a+1)]
=[(a+1)/(a-2)]×[(a²-2)/(a+1)]
=(a²-2)/(a-2)
当a=√2-3时
原式=[(√2-3)²-2]/(√2-3-2)
=(2-6√2+9-2)/(√2-5)
=(9-6√2)(√2+5)/[(√2+5)(√2-5)]
=(9√2+45-12-30√2)/(√2²-5²)
=(33-21√2)/(2-25)
=(33-21√2)/(-23)
=(21√2-33)/23