giúp em 2 câu này : a) `((x+1)/(x-1) -( x-1)/(x+1))/(1+ (x+1)/(x-1))= (x-1)/(2(x+1))` b) `5/x + 4 /(x+1) = 3/ (x+3) + 2/ (x+2)`

Giải thích các bước giải:

a) 

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

`(ĐKXĐ:  x ne ± 1)`

`<=> ((x+1)(x-1)-(x-1)(x+1))/((x-1+x+1)/(x-1))=(x-1)/(2(x+1))`

`<=> (x^2 + 2x + 1 – x^2 + 2x -1) / ((x+1)(x-1)) * (x-1)/(2x) = (x-1)/(2(x+1))`

`(ĐKXĐ: x ne 0)`

`<=> 2/(x+1) = x-1/ (2(x+1))`

`<=> 4 = x-1`

`<=> x = 5`

Vậy `S ={5}`

b) `5/x + 4 /(x+1) = 3/ (x+3) + 2/ (x+2)`

`<=> ( 5/ x + 1) + ( 4/ (x+ 1) +1) = (3/ (x+ 2) + 1) + ( 2/ (x+ 3) + 1)`

`<=>(5+ x) / x + (5+x)/ (x+ 1) = (5+ x)/(x+2) + (5+x)/(x+3)`

`<=> (5+x)(1/x + 1/(x+1)- 1/ (x+2) – 1/ (x+3)) = 0`

`<=> 5+ x = 0`

`<=> x= -5`

Vậy `S= {5}`

≈Học tốt≈