`P = ( (2x-3)/(4x^2 - 12x+5)+(2x-8)/(13x-2x^2-20) -3/(2x-1)) : (21+2x-8x^2)/(4x^2+4x-3) +1`

`= ( (2x-3)/((2x-1)(2x-5)) - (2(x-4))/((2x-5)(x-4)) - 3/(2x-1) ) . (4x^2+4x-3)/(-8x^2+2x+21) + 1`

`= (  (2x-3)/((2x-1)(2x-5)) - 2/(2x-5) - 3/(2x-1) ) . ((2x-1)(2x+3))/(-(4x-7)(2x+3)) +1`

` = ( (2x-3) - 2 (2x-1) - 3 (2x-5))/((2x-1)(2x-5)) . (-(2x-1))/(4x-7) +1`

`=  (2x - 3 - 4x + 2 - 6x + 15)/((2x-1)(2x-5)) . (-(2x-1))/(4x-7)+1`

` = (-8x +14)/((2x-1)(2x-5))  . (-(2x-1))/(4x-7)+1`

`= (-2 (4x-7))/((2x-1)(2x-5)) . (-(2x-1))/(4x-7) +1`

` = 2/(2x-5)  +1`

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

Giải thích các bước giải:

Ta phân tích:

`4x^2 -12x+5=4x^2 -10x-2x+5=2x(2x-5)-(2x-5)=(2x-1)(2x-5)`

`13x-2x^2 -20=-2x^2 +8x+5x-20=-2x(x-4)+5(x-4)=-(x-4)(2x-5)`

`21+2x-8x^2 =-8x^2 +14x-12x+21=-2x(4x-7)-3(4x-7)=-(4x-7)(2x+3)`

`4x^2 +4x-3=4x^2 +6x-2x-3=2x(2x+3)-(2x+3)=(2x+3)(2x-1)`

`P=((2x-3)/(4x^2 -12x+5)+(2x-8)/(13x-2x^2 -20)-3/(2x-1)):(21+2x-8x^2)/(4x^2 +4x-3)+1` `(x \ne 1/2 ;5/2 ;4;-3/2 ;7/4)`

`=((2x-3)/((2x-1)(2x-5))-(2(x-4))/((x-4)(2x-5))-3/(2x-1)):-((4x-7)(2x+3))/((2x+3)(2x-1))+1`

`=((2x-3)/((2x-1)(2x-5))-(2(2x-1))/((2x-1)(2x-5))-(3(2x-5))/((2x-1)(2x-5))). (-(2x-1)/(4x-7))+1`

`=(2x-3-4x+2-6x+15)/((2x-1)(2x-5)) . (-(2x-1)/(4x-7)) +1`

`=(14-8x)/(2x-5) . -1/(4x-7) +1`

`=(-2(4x-7))/(2x-5) . -1/(4x-7) +1`

`=((-2).(-1))/(2x-5) +(2x-5)/(2x-5)`

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

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