Cho ab=1. Chứng minh đẳng thức a(b+1)+b(a+1)=(a+1)(b+1)

`a(b+1)+b(a+1)=(a+1)(b+1)`

Xét VT: `a(b+1)+b(a+1)`

`= ab+a+ba+b`

`= 1+a+1+b`

`= 2+a+b`

Xét VP: `(a+1)(b+1)`

`= ab+a+b+1`

`= 1+a+b+1`

`= 2+a+b`

Vậy `VP=VT (đpcm)`

Hoặc

`a(b+1)+b(a+1)=(a+1)(b+1)`

`=> ab+a+ba+b=ab+a+b+1`

`=> 1+a+1+b=1+a+b+1`

`=> 2+a+b=2+a+b (đpcm)`