a) ` [ x - 1 ] / [ y + 1 ] + [ 2x + 1 ] / [ y + 1 ] ` ( ` ĐK : y ` $\ne$ ` - 1 ) `

` = [ ( x - 1 ) + ( 2x + 1 ) ] / [ y + 1 ] `

` = [ 2x + x - 1 + 1 ] / [ y + 1 ] `

` = [ 3x ] / [ y + 1 `

b) ` ( x / [ x + y ] + y / [ x - y ] ) . ( x² - y² ) ` ( ` ĐK : x ` $\ne$ ` ±y ) `

` = [ [ x ( x - y ) ] / [ ( x + y ) ( x - y ) ] + [ y ( x + y ) ] / [ ( x - y ) ( x + y ) ] ] . ( x² - y² ) `

` = [ x ( x - y ) + y ( x + y ) ] / [ ( x - y ) ( x + y ) ] . ( x² - y² ) `

` = [ x² - xy + xy + y² ] / [ x² - y² ] . ( x² - y² ) `

` = x² - xy + xy + y² `

` = x² + y² `

Đáp án+Giải thích các bước giải:

`a)` `(x-1)/(y+1)+(2x+1)/(y+1) (y \ne -1)`

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

`=(3x)/(y+1)`

`b)` `(x/(x+y)+y/(x-y)) . (x^2-y^2) (x \ne +-y)`

`=[[x(x-y)]/[(x+y)(x-y)]+[y(x+y)]/[(x+y)(x-y)]] . (x+y)(x-y)`

`=[(x^2-xy)/[(x+y)(x-y)]+ (xy+y^2)/[(x+y)(x-y)]] . (x+y)(x-y)`

`=(x^2-xy+xy+y^2)/[(x+y)(x-y)] . (x+y)(x-y)`

`=(x^2+y^2)/[(x+y)(x-y)] . (x+y)(x-y)`

`=[(x^2+y^2)(x+y)(x-y)]/[(x+y)(x-y)]`

`=x^2+y^2`