Question

先化简,再求值：x的平方-y的平方分之x的平方+2xy+y的平方除一x-y分之x的平方+xy,其中x=√2-1,y=√2

Answer 1

x的平方-y的平方分之x的平方+2xy+y的平方除一x-y分之x的平方+xy,其中x=√2-1,y=√2+1

=(x+y)^2/(x+y)(x-y) /((x^2+xy)/(x-y))

=(x+y)/(x-y) * (x-y)/x(x+y)

=1/x

=1/(√2-1)

=√2+1