Rút gọn H=4x/x^2+2x + 3/2-x + 12x/x^3-4x M=6x/x^2-9 - 5x/3-x + x/x+3 S=2y - 6xy+2y/3x+2y + 2y-9x^2/3x+2y U=1-2x/2x + 2x/2x-1 + 1/2x-4x^2

`\text{Đáp án + Giải thích các bước giải :}`

-------------------

`H = (4x)/(x^2 + 2x) + 3/(2-x) + (12x)/(x^3-4x)` ĐKXĐ : `x \ne 2, x \ne - 2` .

    `= (4x)/(x(x + 2)) - 3/(x-2) + (12x)/(x(x^2-4))`

    `= (4x(x-2))/(x(x+2)(x-2)) - (3x(x+2))/(x(x+2)(x-2)) + (12x)/(x(x+2)(x-2))`

    `= 4x(x-2) - 3x(x+2)+ 12x`

    `= 4x^2 - 8x - 3x^2 - 6x + 12x`

    `= x^2 - 2x`

    `= x ( x - 2 )` .

-------------------

`M = (6x)/(x^2-9) - (5x)/(3-x) + x/(x+3)` ĐKXĐ : `x \ne 3, x \ne - 3` .

    `= (6x)/((x-3)(x+3)) + (5x(x+3))/((x-3)(x+3)) + (x(x-3))/((x-3)(x+3))`

    `= 6x + 5x(x+3) + x(x-3)`

    `= 6x + 5x^2 + 15x + x^2 - 3x`

    `= 6x^2 + 18x`

    `= 6x (x + 3)` .

-------------------

` S = 2y - (6xy+2y)/(3x+2y) + (2y - 9x^2)/(3x+2y)` ĐKXĐ : `3x \ne - 2y` .

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

    `= 2y - (6xy+2y-2y+9x^2)/(3x+2y)`

    `= 2y - (9x^2+6xy)/(3x+2y)`

    `= 2y - (3x(3x + 2y))/(3x+2y)`

    `= 2y - 3x` .

-------------------

` U = (1-2x)/(2x) + (2x)/(2x-1) + 1/(2x - 4x^2)` ĐKXĐ : `x \ne 0, x \ne 1/2` .

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

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

     `= ( 1 - 2x ) ( 2x - 1 ) + 4x^2 - 1`

     `= 2x - 1 - 4x^2 + 2x + 4x^2 - 1`

     `= 4x + 2`

     `= 2 ( 2x + 1 )` .

-------------------

`\text{CHÚC BN HOC TỐT<3}`