$#nobody$

`{(x/(x - 5) + y/(y - 6) = 5(1)),(10/(x - 5) - 9/(y - 6) = - 1(2)):} (x \ne 5 ; y \ne 6)`

 `(1) <=> (x - 5 + 5)/(x - 5) + (y - 6 + 6)/(y - 6) = 5`

`<=> 1 + 5/(x - 5) + 1 + 6/(y - 6) = 5`

`<=> 5/(x - 5) + 6/(y - 6) = 3(3)`

Từ `(2) ; (3)`

`=> {(10/(x - 5) - 9/(y - 6) = - 1),(5/(x - 5) + 6/(y - 6) = 3):}`

`<=> {(10/(x - 5) - 9/(y - 6) = - 1),(10/(x - 5) + 12/(y - 6) = 6):}`

`<=> {(21/(y - 6) = 7),(5/(x - 5) + 6/(y - 6) = 3):}`

`<=> {(y - 6 = 3),(5/(x - 5) + 6 . 1/3 = 3):}`

`<=> {(y - 6 = 3),(5/(x - 5) = 1):}`

`<=> {(x - 5 = 5),(y - 6 = 3):}`

`<=> {(x = 10(tm)),(y = 9(tm)):}`

Vậy : `(x ; y) = (10 ; 9)`