Question

已知x=(1-a)/(1+a),y=(3-2a)/(2-3a),请用x的代数式表示y

Answer 1

x=(1-a)/(1+a)

x+1=(1-a)/(1+a)+1=(1-a+1+a)/(1+a)=2/(1+a)

1+a=2/(x+1)

a=2/(x+1)-1=(2-x-1)/(x+1)=(1-x)/(x+1)

所以y=[3-2(1-x)/(x+1)]/[2-3(1-x)/(x+1)]

分子分母同乘x+1

y=[3(x+1)-2(1-x)]/[2(x+1)-3(1-x)]

y=(5x+1)/(5x-1)