Đáp án:

 

Giải thích các bước giải:

 $a,\dfrac{20x(2x-1)}{6x^{2}(1-2x)^{2}}$

$=\dfrac{2x.10(2x-1)}{2x.3x(2x-1)^{2}}$

$=\dfrac{10}{3x(2x-1)}$

$b,\dfrac{4x^{2}-y^{2}}{2x^{2}-3xy+y^{2}}$

$=\dfrac{(2x-y)(2x+y)}{2x(x-y)-y(x-y)}$

$=\dfrac{(2x-y)(2x+y)}{(x-y)(2x-y)}$

$=\dfrac{2x+y}{x-y}$

(Bài tham khảo)

Đáp án + giải thích các bước giải:

Câu `9`:

`a, (20x(2x - 1))/(6x^2(1 - 2x)^2)`

` = 10/(3x(2x - 1)`

` = 10/(6x^2 - 3x)`

`b, (4x^2 - y^2)/(2x^2 - 3xy + y^2)`

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

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

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

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

Câu `10`:

`a, (x + 1)/(2x + 6) + (2x + 3)/(x^2 + 3x)`

` = ( x(x + 1))/( 2x(x + 3)) + ( 2(2x + 3))/( 2x(x + 3))`

` = (x^2 + x + 4x +3)/( 2x^2 + 6x)`

` = ( x^2 + 5x + 3)/(2x^2 + 6x)`

`b, 4/(x + 2) + 3/(x - 2) + (5x + 2)/(4 - x^2)`

` = ( 4(x - 2))/( (x + 2)(x -2)) + ( 3(x + 2))/( (x - 2)(x + 2)) - (5x + 2)/(x^2 - 4)`

` = (4x - 8 + 3x + 6 - 5x - 2)/( (x + 2)(x - 2))`

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

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

` = 2/(x + 2)`