Question

已知方程7/4x=3-2/y. ①用含x的代数式表示y； ②用含y的代数式表示x.

Answer 1

解1：

7/(4x)=3-2/y

[7/(4x)]×y=[3-2/y]×y

(7y)/(4x)=3y-2

[(7y)/(4x)]-3y=3y-2-3y

[7/(4x)-3]y=-2

[(7-12x)/(4x)]y=-2

[(7-12x)/(4x)]y×[4x/(7-12x)]=-2×[4x/(7-12x)]

y=8x/(7-12x)

解2：

7/(4x)=3-2/y

[7/(4x)]×4x=(3-2/y)×4x

7=[(3y-2)/y]×4x

4x[(3y-2)/y]=7

4x[(3y-2)/y]×[y/(3y-2)]=7×[y/(3y-2)]

4x=7y/(3y-2)

4x÷4=[7y/(3y-2)]÷4

x=7y/[4(3y-2)]

x=7y/(12y-8)