`e)`

`\frac{x-1}{59}+\frac{x-2}{58}+\frac{x-3}{57}=\frac{x-4}{56}+\frac{x-5}{55}+\frac{x-6}{54}`

`<=>(\frac{x-1}{59}-1)+(\frac{x-2}{58}-1)+(\frac{x-3}{57}-1)=(\frac{x-4}{56}-1)+(\frac{x-5}{55}-1)+(\frac{x-6}{54}-1)`

`<=>\frac{x-60}{59}+\frac{x-60}{58}+\frac{x-60}{57}=\frac{x-60}{56}+\frac{x-60}{55}+\frac{x-60}{54}`

`<=>\frac{x-60}{59}+\frac{x-60}{58}+\frac{x-60}{57}-\frac{x-60}{56}-\frac{x-60}{55}-\frac{x-60}{54}=0`

`<=>(x-60)(\frac{1}{59}+\frac{1}{58}+\frac{1}{57}-\frac{1}{56}-\frac{1}{55}-\frac{1}{54})=0`

Mà `\frac{1}{59}+\frac{1}{58}+\frac{1}{57}-\frac{1}{56}-\frac{1}{55}-\frac{1}{54}=0`

`<=>x-60=0`

`<=>x=60`

`f)`

`\frac{59-x}{41}+\frac{57-x}{43}+\frac{55-x}{45}+\frac{53-x}{47}+\frac{51-x}{49}=-5`

`<=>\frac{59-x}{41}+1+\frac{57-x}{43}+1+\frac{55-x}{45}+1+\frac{53-x}{47}+1+\frac{51-x}{49}+1=0`

`<=>\frac{100-x}{41}+\frac{100-x}{43}+\frac{100-x}{45}+\frac{100-x}{47}+\frac{100-x}{49}=0`

`<=>(100-x)(\frac{1}{41}+\frac{1}{43}+\frac{1}{45}+\frac{1}{47}+\frac{1}{49})=0`

Mà `\frac{1}{41}+\frac{1}{43}+\frac{1}{45}+\frac{1}{47}+\frac{1}{49}=0`

`<=>100-x=0`

`<=>x=100`

`g)`

`\frac{x-5}{2020}+\frac{x-15}{2010}+\frac{x-25}{2000}=\frac{x-2020}{5}+\frac{x-2010}{15}+\frac{x-2000}{25}`

`<=>\frac{x-5}{2020}-1+\frac{x-15}{2010}-1+\frac{x-25}{2000}-1=\frac{x-2020}{5}-1+\frac{x-2010}{15}-1+\frac{x-2000}{25}-1`

`<=>x-2025=0`

`<=>x=2025`

`h)`

`\frac{x+14}{86}+\frac{x+15}{85}+\frac{x+16}{84}+\frac{x+17}{83}+\frac{x+116}{4}=0`

`<=>\frac{x+14+86}{86}-\frac{86}{86}+\frac{x+15+85}{85}-\frac{85}{85}+\frac{x+16+84}{84}-\frac{84}{84}+\frac{x+17+83}{83}-\frac{83}{83}+\frac{x+100}{4}+\frac{16}{4}=0`

`<=>\frac{x+100}{86}+\frac{x+100}{85}+\frac{x+100}{83}+\frac{x+100}{4}=0`

`<=>(x+100)(\frac{1}{86}+\frac{1}{85}+\frac{1}{84}+\frac{1}{83}+\frac{1}{4})=0`

`<=>x+100=0`

`<=>x=-100`

 

Đáp án:

`e)` `( x - 1 ) / 59 + ( x - 2 ) / 58 + ( x - 3 ) / 57 = ( x - 4 ) / 56 + ( x - 5 ) / 55 + ( x - 6 ) / 54`

`<=> ( x - 1 ) / 59 - 1 + ( x - 2 ) / 58 - 1 + ( x - 3 ) / 57 - 1 = ( x - 4 ) / 56 - 1 + ( x - 5 ) / 55 - 1 + ( x - 6 ) / 54 - 1`

`<=> ( x - 60 ) / 59 + ( x - 60 ) / 58 + ( x - 60 ) / 57 = ( x - 60 ) / 56 + ( x - 60 ) / 55 + ( x - 60 ) / 54`

`<=> ( x - 60 ) / 59 + ( x - 60 ) / 58 + ( x - 60 ) / 57 - ( x - 60 ) / 56 + ( x - 60 ) / 55 + ( x - 60 ) / 54 = 0`

`<=>` `( x - 60 ) . ( 1/59 + 1/58 + 1/57 - 1/56 + 1/55 + 1/54 ) = 0`

Mà  `1/59 + 1/58 + 1/57 - 1/56 + 1/55 + 1/54 > 0`

`<=>` `x - 60 = 0`

`<=>` `x = 60`

Vậy  `x = 60`.

`f)` `( 59 - x ) / 41 + ( 57 - x ) / 43 + ( 55 - x ) / 45 + ( 53 - x ) / 47 + ( 51 - x ) / 49 = -5`

`<=> ( 59 - x ) / 41 + 1 + ( 57 - x ) / 43 + 1 + ( 55 - x ) / 45 + 1 + ( 53 - x ) / 47 + 1 + ( 51 - x ) / 49 + 1 = 0`

`<=> ( 100 - x ) / 41 + ( 100 - x ) / 43 + ( 100 - x ) / 45 + ( 100 - x ) / 47 + ( 100 - x ) / 49 = 0`

`<=> ( 100 - x ) . ( 1/41 + 1/43 + 1/45 + 1/47 + 1/49 ) = 0`

Mà  `1/41 + 1/43 + 1/45 + 1/47 + 1/49 = 0`

`<=>` `100 - x = 0`

`<=>` `x = 100`

Vậy  `x = 100`.