Question

请从下列三个式子中任选两个构成一个分式,并化简该分式:y+xy,xy-y,x²-1

Answer 1

y+xy=y(1+x)

xy-y=y(x-1)

x²-1=(x+1)(x-1)

(y+xy)/(x²-1)=y(1+x)/(x+1)(x-1)=y/(x-1)

(xy-y)/(x²-1)=y(x-1)/(x+1)(x-1)=y/(x+1)

(y+xy)/(xy-y)=y(x+1)/y(x-1)=(x+1)/(x-1)=(x-1+2)/(x-1)=1 - 2/(x-1)