a) $\frac{x+1}{2015}$+$\frac{x+2}{2014}$=$\frac{x+3}{2013}$+$\frac{x+4}{2012}$ b) $\frac{x-85}{15}$+$\frac{x-74}{13}$+$\frac{x-67}{11}$+$\frac{x-64}{9}$=10 giải theo chi tiết, theo kiểu phân số giúp e ạ, e cảm ơn

`a) ( x + 1 )/2015 + ( x + 2 )/2014 = ( x + 3 )/2013 + ( x + 4 )/2012`

`⇔ ( ( x + 1 )/2015 + 1 ) + ( ( x + 2 )/2014 + 1 ) = ( ( x + 3 )/2013 + 1 ) + ( ( x + 4)/2012 + 1 )`

`⇔ ( x + 2016 )/2015 + ( x + 2016 )/2014 = ( x + 2016 )/2013 + ( x + 2016 )/2012`

`⇔ ( x + 2016 )/2015 + ( x + 2016 )/2014 - ( x + 2016 )/2013 - ( x + 2016 )/2012 = 0`

`⇔ ( x + 2016 ) . ( 1/2015 + 1/2014 - 1/2013 - 1/2012 ) = 0`

Do `1/2015 + 1/2014 < 1/2013 + 1/2021 ⇒ 1/2015 + 1/2014 - 1/2013 - 1/2012 < 0`

`⇔ x + 2016 = 0`

`⇔ x = - 2016`

Vậy `, x = - 2016 .`

`b) ( x - 85 )/15 + ( x - 74 )/13 + ( x - 67 )/11 + ( x - 64 )/9 = 10`

`⇔ ( x - 85 )/15 + ( x - 74 )/13 + ( x - 67 )/11 + ( x - 64 )/9 - 10 = 0`

`⇔ ( ( x - 85 )/15 - 1 ) + ( ( x - 74 )/13 - 2 ) + ( ( x - 67 )/11 - 3 ) + ( ( x - 64 )/9 - 4 ) = 0`

`⇔ ( x - 100 )/15 + ( x - 100 )/13 + ( x - 100 )/11 + ( x - 100 )/9 = 0`

`⇔ ( x - 100 ) . ( 1/15 + 1/13 + 1/11 + 1/9 ) = 0`

`⇔ x - 100 = 0 (` Do `1/15 + 1/13 + 1/11 + 1/9 > 0 )`

`⇔ x = 100`

Vậy `, x = 100 .`