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Đặt `a/b=c/d=k (k \ne 0)`
`->a=bk,c=dk`
iii,
`(5a+2b)/(5a-2b)`
`= (5bk +2b)/(5bk - 2b)`
`= (b(5k+2) )/(b (5k-2) )`
`= (5k+2)/(5k-2)` (1)
`(5c+2d)/(5c-2d)`
`= (5dk +2d)/(5dk - 2d)`
`= (d(5k+2) )/(d (5k-2) )`
`= (5k+2)/(5k-2)` (2)
Từ (1), (2)
`-> (5a+2b)/(5a-2b) = (5c+2d)/(5c-2d)`
iv,
`(a^2 +c^2)/(b^2+d^2)`
`= (b^2k^2 + d^2k^2)/(b^2 +d^2)`
`= (k^2 (b^2 +d^2) )/(b^2 +d^2)`
`=k^2` (1)
`(a+c)^2/(b+d)^2`
`= (bk+dk)^2/(b+d)^2`
`= [k (b+d)]^2/(b+d)^2`
`= (k^2 (b+d)^2 )/(b+d)^2`
`= k^2` (2)
Từ (1), (2)
`->(a^2 +c^2)/(b^2 +d^2) = (a+c)^2/(b+d)^2`
