Question

先化简,再求值：x+1/x的平方+1÷（x+1）的三次方/x的四次方-1-(x-3)/(x+1),其中x=√3+1

Answer 1

原式=(x+1)/(x²+1)×(x²+1)(x²-1)/(x+1)³-(x-3)/(x+1)

=(x²-1)/(x+1)²-(x-3)/(x+1)

=(x²-1-x²+2x+3)/(x+1)²

=2(x+1)/(x+1)²

=2/(x+1)

=2/(√3+1+1)

=4-2√3