`a_1)`
`a/b=c/d`
`⇔ad=bc`
`⇔ad+bd=bc+bd`
`⇔d(a+b)=b(c+d)`
`⇔(a+b)/b=(c+d)/d`
`a_2)`
`a/b=c/d`
`⇔ad=bc`
`⇔ad-bd=bc-bd`
`⇔d(a-b)=b(c-d)`
`⇔(a-b)/b=(c-d)/d`
b)
Đặt: `a/b=c/d=k`
`⇒a=bk`
`c=dk`
Biểu thức `⇒(5bk+3b)/(5bk-3b)=(5dk+3d)/(5dk-3d)`
`⇔[b(5k+3)]/[b(5k-3)]=[d(5k+3)]/[d(5k-3)]`
`⇔(5k+3)/(5k-3)=(5k+3)/(5k-3)` (hiển nhiên)
`⇒đpcm`