Выполнить указанные действия: 1) (4x-3)/(3-2x)-(4+5x)/(3+2x)-(3+x-10x^2)/(4x^2-9); 2)(4a^2-3a+5)/(a^3-1)-(1-2a)/(a^2+a+1)+(6)/(1-a);

Выполним указанные действия: 

1) (4x - 3)/(3 - 2x) - (4 + 5x)/(3 + 2x) - (3 + x - 10x^2)/(4x^2 - 9) = (-(4x – 3) * (2x + 3) – (4 + 5x) * (2x – 3) -3 – x + 10x^2)/(4x^2 – 9) = (-8x^2 – 6x + 9 - 8x + 12 – 10x^2 + 15x – 3 – x + 10x^2)/(4x^2 – 9) = (-8x^2 + 20)/(4x^2 – 9);

2) (4a^2 - 3a + 5)/(a^3 - 1) - (1 - 2a)/(a^2 + a + 1) + (6)/(1- a) =  (4a^2 - 3a + 5 – (1 – 2a)(a – 1) – 6(a^2 + a + 1))/(a^3 – 1) = (4a^2 - 3a + 5 – a + 1 + 2a^2 – 2a  – 6a^2 - 6 a - 6))/(a^3 – 1) =

 (-12a)/(a^3 – 1);

3) (2a - 1)/(2a) - (2a)/(2a - 1) - (1)/(2a - 4a^2) =  (2a - 1)/(2a) +  (2a)/(1 – 2a) - (1)/(2a - 4a^2) =  

(-4a^2 + 4a – 1 + 4a^2 – 1)/(2a – 4a^2) = (4a – 2)/(2a – 4a^2) = -2(1 – 2a)/(2a(1 – 2a)) = -1/a;

4) (1)/(6x - 4y) - (1)/(6x + 4y) - (3x)/(4y^2 - 9x^2) = (1)/(6x - 4y) - (1)/(6x + 4y) + (3x)/(9x^2 – 4y^2) = (3x + 2y – 3x +2y – 6x)/(2 * (9x^2 – 4y^2)) = ( 4y – 6x)/(2 * (9x^2 – 4y^2)) = ( 2y – 3x)/(9x^2 – 4y^2) = -1/(3x + 2y);

5) (3a+2)/(a^2 - 2a + 1) - (6)/(a^2 - 1) - (3a - 2)/(a^2 + 2a + 1) = ((3a + 2) * (a + 1)^2 – 6 * (a^2 – 1) – (3 * a – 2) * (a – 1)^2)/(a^2  + 1) * (a^2 – 1)) = (6a^3 + 6a^2 + 4a – 6a^2 + 6)/((a^2 – 1) * (a^2 + 1)^2) = (6a^3 + 4a + 6)/(a^4 – 1)^2.

6) (1)/(a - b) - (3ab)/(a^3 - b^3) - (b - a)/(a^2 + ab + b^2) = (a^2 + ab + b^2 – 3ab – (b – a) * (a – b))/(a^3 – b^3) = (a^2 + ab + b^2 – 3ab  + a^2 – b^2)/(a^3 – b^3) = (2a^2 – 2ab)/(a^3 – b^3)  = 2a/(a^2  + ab + b^2).