`d) 1/(1 xx 3) + 1/(3 xx 5) + 1/(5 xx 7) + ... + 1/(49 xx 51)`
`= 1/2 xx 2 xx (1/(1 xx 3) + 1/(3 xx 5) + 1/(5 xx 7) + ... + 1/(49 xx 51))`
`= 1/2 xx (2/(1 xx 3) + 2/(3 xx 5) + 2/(5 xx 7) + ... + 2/(49 xx 51))`
`= 1/2 xx (1 - 1/3 + 1/3 - 1/5 + 1/5 x 1/7 + ... + 1/49 - 1/51)`
`= 1/2 xx (1 - 1/51)`
`= 1/2 xx (51/51 - 1/51)`
`= 1/2 xx 50/51`
`= 25/51`
Áp dụng: `(y - x)/(x xx y) = 1/x - 1/y`
`b) (x - 1/2) xx 5/3 = 7/4 - 1/2`
`=> (x - 1/2) xx 5/3 = 5/4`
`=> x - 1/2 = 5/4 : 5/3`
`=> x - 1/2 = 3/4`
`=> x = 3/4 + 1/2`
`=> x = 5/4`
Vậy `x = 5/4`
`d) 71 + 65 xx 4 = (x + 140)/x + 260`
`=> 71 + 260 = x/x + 140/x + 260`
`=> 331 = 1 + 140/x + 260`
`=> 331 = 140/x + 261`
`=> 140/x = 331 - 261`
`=> 140/x = 70`
`=> 140/x = 140/2`
`=> x = 2`
Vậy `x = 2`
