Giải các phương trình sau

`a)`

`(x+2)/98 + (x+3)/97 = (x+4)/96 + (x+5)/95`

`<=> ((x+2)/98 +1) + ((x+3)/97 +1) = ((x+4)/96 +1) + ((x+5)/95 +1)`

`<=> (x+100)/98 + (x+100)/97 = (x+100)/96 + (x+100)/95`

`<=>(x+100)(1/98 + 1/97 - 1/96 - 1/95)=0`

Vì `1/98 + 1/97 - 1/96 - 1/95 \ne 0`

`<=> x+100=0`

`<=>x=-100`

Vậy `S={-100}`.

`b)`

`(x-1)/2004 + (x-2)/2003 = (x-3)/2002 + (x-4)/2001`

`<=>((x-1)/2004 -1) + ((x-2)/2003 -1) = ((x-3)/2002 -1) + ((x-4)/2001 -1)=0`

`<=> (x-2005)/2004 + (x-2005)/2003 = (x-2005)/2002 + (x-2005)/2001`

`<=> (x-2005)(1/2004 + 1/2003 - 1/2002 - 1/2001) =0`

Vì `1/2004 + 1/2003 - 1/2002 - 1/2001 \ne 0`

`<=>x-2005=0`

`<=>x=2005`

Vậy `S={2005}`.

`c)`

`(201-x)/99 + (203-x)/97 + (205-x)/95 +3=0`

`<=> ((201-x)/99 +1) + ((203-x)/97 +1) + ((205-x)/95 +1) =0`

`<=> (300-x)/99 + (300-x)/97 + (300-x)/95 =0`

`<=>(300-x)(1/99 + 1/97 + 1/95) =0`

Vì `1/99 + 1/97 + 1/95 \ne 0`

`<=>300-x=0`

`<=>x=300`

Vậy `S={300}`.

`d)`

`(x-45)/55 + (x-47)/53 = (x-55)/45 + (x-53)/47`

`<=> ((x-45)/55 -1) + ((x-47)/53 -1) = ((x-55)/45 -1) + ((x-53)/47 -1)`

`<=> (x-100)/55 + (x-100)/53 = (x-100)/45 + (x-100)/47`

`<=>(x-100)(1/55 + 1/53 - 1/45 - 1/47) =0`

Vì `1/55 + 1/53 - 1/45 - 1/47 \ne 0`

`<=>x-100=0`

`<=>x=100`

Vậy `S={100}`.

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