Question

化简{(a/a-1)-(2/a平方-1)}÷{1-(1/a+1)},再代入一个合适的a值求该代数式的值

求达人解答啊

Answer 1

{a/(a-1)-2/(a^2*1)}÷{1-1/(a+1)}

={a(a+1)/(a^2-1)-2/(a^2*1)}÷{a/(a+1)}

={(a^2+a-2)/(a^2-1)}÷{a/(a+1)}

={(a+2)(a-1)/(a^2-1)}÷{a/(a+1)}

={(a+2)/(a+1)}÷{a/(a+1)}

=(a+2)/(a+1)*(a+1)/a

=(a+2)/a

=1+2/a

令a=2

原式=1+2/a=1+2/2=1+1=2