`a) ( 20x^2 - 45 )/( 4x^2 + 12x + 9 )  (  Đk  :  x \ne -3/2 )`

`= ( 5 ( 4x^2 - 9 ))/( 4x^2 + 2 . 3 . 2x + 9 )`

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

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

Áp dụng hằng đẳng thức :

`A^2 + 2AB + B^2 = ( A + B )^2`

`A^2 - B^2 = ( A + B )( A - B )`

`b) ( 5x^2 - 10xy )/( 8y^3 - 12xy^2 + 6xy^2 - x^3 )  (  Đk  :  x \ne 2y  )`

`= ( 5x( x - 2y ))/( 2y - x )^3`

`= - ( 5x( x - 2y ))/( x - 2y )^3`

`= - ( 5x )/( x - 2y )^2`

Áp dụng hằng đẳng thức : `A^3 - 3A^2B + 3AB^2 - B^3 = ( A - B )^3`

`c) ( 80x^3 - 125x )/( 3x - 9 - ( x - 3 )( 8 - 4x ) )  (  Đk  :  x \ne 3 ; x \ne 5/4  )`

`= ( 5x ( 16x^2 - 25 ))/( 3 ( x - 3 ) - ( x - 3 )( 8 - 4x ) )`

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

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

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

Áp dụng hằng đẳng thức : `A^2 - B^2 = ( A + B )( A - B )`

`d) ( 9 - ( x + 5 )^2 )/( x^2 + 4x + 4 )  (  Đk  : x \ne -2  )`

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

`= (( x + 8 )( - x - 2 ))/( x + 2 )^2`

`= - (( x + 8 )( x + 2 ))/( x + 2 )^2`

`= - ( x + 8 )/( x + 2 )`

Áp dụng hằng đẳng thức :

`A^2 + 2AB + B^2 = ( A + B )^2`

`A^2 - B^2 = ( A + B )( A - B )`

Đáp án+Giải thích các bước giải:

 `a)(20x^2-45)/(4x^2+12x+9)`  `(ĐK: x\ne-3/2)`

`=[5(4x^2-9)]/[(2x)^2+2.2x.3+3^2]`

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

`=[5(2x-3)]/(2x+3)`

`=(10x-15)/(2x+3)`

`b)(5x^2-10xy)/(8y^3-12xy^2+6x^2 y-x^3)`   `(ĐK:x \ne 2y)`

`=[5x(x-2y)]/[(2y)^3-3(2y)^2 .x+3.2y.x^2-x^3]`

`=[-5x(2y-x)]/[(2y-x)^3]`

`=-(5x)/(2y-x)^2`

`c)(80x^3-125x)/[3x-9-(x-3)(8-4x)]`  `(ĐK: x \ne 3;x\ne5/4)`

`=[5x(16x^2-25)]/[3(x-3)-(x-3)(8-4x)]`

`=[5x[(4x)^2-5^2]]/[(x-3)(3-8+4x)]`

`=[5x(4x-5)(4x+5)]/[(x-3)(4x-5)]`

`=[5x(4x+5)]/(x-3)`

`=(20x^2+25x)/(x-3)`

`d)[9-(x+5)^2]/(x^2+4x+4)`  `(ĐK: x\ne -2)`

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

`=[(-x-2)(x+8)]/(x+2)^2`

`=[-(x+2)(x+8)]/(x+2)^2`

`=(-x-8)/(x+2)`