`(1/2 + 1/3 + 1/4 + ... + 1/9 + 1/10)x = 1/9 + 2/8 + 3/7 + ... + 8/2 + 9/1`

`( 1/2 + 1/3 + 1/4 + ... + 1/9 + 1/10 )x = 1/9 + 2/8 + 3/7 + ... + 8/2 + 9/1`

`<=> x = ( 1/9 + 2/8 + 3/7 + ... + 8/2 + 9/1 )/( 1/2 + 1/3 + 1/4 + ... + 1/9 + 1/10 )`

`<=> x = ( 1/9 + 2/8 + 3/7 + ... + 8/2 + (\underbrace{1 + 1 + ... + 1}_{\text{9 chữ số 1}}))/( 1/2 + 1/3 + 1/4+ ... + 1/9 + 1/10`

`<=> x = ( ( 1/9 + 1 ) + ( 2/8 + 1 ) + ( 3/7 + 1 ) + ... + ( 8/2 + 1 ) + 1 )/( 1/2 + 1/3 + 1/4 + ... + 1/9 + 1/10 )`

`<=> x = ( 10/9 + 10/8 + 10/7 + ... + 10/2 + 10/10 )/( 1/2 + 1/3 + 1/4 + ... + 1/9 + 1/10 )`

`<=> x = ( 10 ( 1/10 + 1/9 + 1/8 + 1/7 + ... + 1/2 ))/( 1/2 + 1/3 + 1/4 + ... + 1/9 + 1/10 )`

`<=> x = 10`

Vậy `x = 10`