Chứng minh rằng nếu `a/b = c/d` thì: `(5a + 3b)/(5a - 3b) = (5c + 3d)/(5c - 3d)`

Sửa đề : `(5a+33b)/(5a-3b) to (5a+3b)/(5a-3b)`

Đặt `a/b=c/d=k`

`to {(a=bk),(c=dk):}`

`=>`

`(5a+3b)/(5a-3b) \ = (5bk+3b)/(5bk-3b)`

`\qquad\qquad\qquad\qquad=(b(5k+3))/(b(5k-3))=(5k+3)/(5k-3) \ \ (2)`

`(5c+3d)/(5c-3d) \ = (5dk+3d)/(5dk-3d)`

`\qquad\qquad\qquad\qquad=(d(5k+3))/(d(5k-3))=(5k+3)/(5k-3) \ \ (2)`

 Từ `(1)` và `(2) to (5a+3b)/(5a-3b)=(5c+3d)/(5c-3d)`