`a) A = ((x+1)/(x-1) - (x-1)/(x+1)) : (2x)/(5x-5) (ĐKXĐ : x \ne +-1)`
`= (((x+1).(x+1))/((x-1).(x+1)) - ((x-1).(x-1))/((x+1).(x-1)) ): (2x)/(5.(x-1))`
` = ((x+1)^2 - (x-1)^2)/((x-1).(x+1)) . (5.(x-1))/(2x)`
` = ((x^2 + 2x+1) - (x^2 - 2x+1))/((x-1).(x+1)) . (5.(x-1))/(2x)`
` = (x^2 + 2x + 1 - x^2 + 2x - 1)/((x-1).(x+1)) . (5.(x-1))/(2x)`
` = (4x)/((x-1).(x+1)) . (5.(x-1))/(2x)`
` = ( 2 . 2x)/((x-1).(x+1)) . (5.(x-1))/(2x)`
` = (2.5)/(x+1)`
` = 10/(x+1)`
`b)`
Ta có : `A + 6/(x-2) = -1`
`<=> A = -1 - 6/(x-2)`
Để `A + 6/(x+1) = -1` thì `10/(x+1) = -1-6/(x-2)` và `x\ne +-1`
`<=> (10.(x-2))/((x+1).(x-2)) = (-1.(x+1).(x-2))/((x+1).(x-2)) - (6.(x+1))/((x+1).(x-2))`
`=> 10.(x-2) = -1.(x+1).(x-2) - 6.(x+1)`
`<=> 10x - 20 = (-x-1).(x-2) - 6x - 6`
`<=> 10x - 20 = -x^2 + 2x - x + 2 - 6x - 6`
`<=> 10x + x^2 - 2x + x + 6x = 2 - 6 + 20`
`<=> x^2 +15x = 16`
`<=> x^2 + 15x - 16 = 0`
`<=> x^2 - x + 16x - 16 = 0 `
`<=> x.(x-1) + 16.(x-1) = 0`
`<=> (x+16).(x-1) = 0`
`<=> x+16=0` hoặc `x-1=0`
`+)x+16=0 <=> x =-16 (TMĐKXĐ)`
`+) x-1=0 <=> x =1 (KTMĐKXĐ)`
Vậy với `x=-16` thì `A + 6/(x-2) = -1`
