Rút gọn `A` `A= ( (x-2)/(2x-2) + 3/(2x-2) - (x+3)/(2x+2) ) : ( 1 - (x-3)/(x+1) )`

2 câu trả lời

` A =  (  [ x - 2 ] / [ 2x - 2 ]  +  3 / [ 2x - 2 ]  -  [ x + 3 ] / [ 2x + 2 ]  )  :  (  1  -  [ x - 3 ] / [ x + 1 ]  ) `

` A = (  [ x - 2 + 3 ] / [ 2x - 2 ]  -  [ x + 3 ] / [ 2x + 2 ]  )  :  (  [ x + 1 ] / [ x + 1 ]  -  [ x - 3 ] / [ x + 1 ]  ) `

` A = (  [ x + 1 ] / [ 2 ( x - 1 ) ]  -  [ x + 3 ] / [ 2 ( x + 1 ) ]  )  :  [ x + 1 - x + 3 ] / [ x + 1 ] `

` A = [ ( x + 1 )  ( x + 1 ) - ( x + 3 )  ( x - 1 ) ] / [ 2  ( x - 1 )  ( x + 1 ) ]  :  4 / [ x + 1 ] `

` A = [ x² + 2x + 1 - ( x² + 2x - 3 ) ] / [ 2 ( x - 1 ) ( x + 1 ) ]  .  [ x + 1 ] / 4 `

` A = [ x² + 2x + 1 - x² - 2x + 3 ] / [ 2  ( x - 1 ) ]  .  1/4 `

` A = 4 / [ 2 ( x - 1 ) ]  .  1/4 `

` A = 1 / [ 2 ( x - 1 ) ] `

Vậy ` A = 1 / [ 2 ( x - 1 ) ] `

`A=( (x-2)/(2x-2) + 3/(2x-2) - (x+3)/(2x+2)) : (1- (x-3)/(x+1))`

`= [(x+1)/(2(x-1)) - (x+3)/(2(x+1))] : 4/(x+1)`

`= [ ((x+1)^2)/(2(x-1)(x+1)) - ((x+3)(x-1))/(2(x+1)(x-1))] : 4/(x+1)`

`= (x^2+2x+1 - x^2 - 2x + 3)/(2(x^2-1)) . (x+1)/4`

`= 4/(2(x-1)(x+1)) . (x+1)/4`

`= 1/(2(x-1)`

Vậy `A = 1/(2(x-1)`