Đáp án $*$ Giải thích các bước giải:

 `(x+9y)/(x^2 -9y^2) -(3y)/(x^2 +3xy)`

`=(x+9y)/((x-3y)(x+3y)) -(3y)/(x(x+3y)`

`=(x(x+9y))/(x(x-3y)(x+3y)) -(3y(x-3y))/((x(x-3y)(x+3y))`

`=(x^2 +9xy -3xy +9y^2)/(x(x-3y)(x+3y))`

`=(x^2 +6xy +9y^2)/(x(x-3y)(x+3y))`

`=((x+3y)^2)/(x(x-3y)(x+3y))`

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

`6,`

`\frac{x+9y}{x^2-9y^2}-\frac{3y}{x^2+3xy}`

`=\frac{x+9y}{x^2-(3y)^2}-\frac{3y}{x.(x+3y)}`

`=\frac{x+9y}{(x-3y).(x+3y)}-\frac{3y}{x.(x+3y)}`

`=\frac{x.(x+9y)}{x.(x-3y).(x+3y)}-\frac{3y.(x-3y)}{x.(x+3y).(x-3y)}`

`=\frac{x.(x+9y)-[3y.(x-3y)]}{x.(x+3y).(x-3y)}`

`=\frac{x^2+9xy-[3xy-9y^2]}{x.(x+3y).(x-3y)}`

`=\frac{x^2+9xy-3xy+9y^2}{x.(x+3y).(x-3y)}`

`=\frac[x^2+6xy+9y^2}{x.(x+3y).(x-3y)}`

`=\frac{(x+3y)^2}{x.(x+3y).(x-3y)}`

`=\frac{x+3y}{x.(x-3y)}`