`Gọi` ` d=``ƯCLN(2n+7,5n+3)`
`Vì` `n ∈ Z``=>``2n+7,5n+3∈Z``=>``d∈Z``.`
`=>``2n+7` `ch``ia` `hết` `cho` `d`
`5n+3` `ch``ia` `hết` `cho` `d`
`=>``5(2n+7)` `ch``ia` `hết` `cho` `d`
`2(5n+3)` `ch``ia` `hết` `cho` `d`
`=>``15n+35` `ch``ia` `hết` `cho` `d`
`15n+6` `ch``ia` `hết` `cho` `d`
`=>``(15n+35)-(15n+6)` `ch``ia` `hết` `cho` `d`
`=>``29` `ch``ia` `hết` `cho` `d`
`=>` `d ∈Ư(29)={±1;±29}`
`Mặt` `khác:`
`2n+7` `ch``ia` `hết` `cho` `d`
`5n+3` `ch``ia` `hết` `cho` `d`
`=>``(2n+7)+(5n+3 )` `ch``ia` `hết` `cho` `d`
`=>` `7n+10` `ch``ia` `hết` `cho` `d`
`Vì` `7n+10` `không` `ch``ia` `hết` `cho` `±29`
`=>`` d `$\neq$ `±29`
`=>``d ∈{±1}`
`=>` `Phân` `số` $\frac{2n+7}{5n+3}$ `là` `phân` `số` `tối` `giản.`
`Vậy` $\frac{2n+7}{5n+3}$ `là` `phân` `số` `tối` `giản.`
