Question

Exercitiul 4 .....urgent!!!!!!!!

Answer 1

A)  [5/(2x+1)-1/(x+1) -1/(2x²+3x+1)] / [(3x-6)/(2x²-x-1)] =
{[5(x+1)-(2x+1)-1] / [(x+1)(x+2)]} / [(3x-6)/(2x²-x-1) =
{(5x+5-2x-1-1) / [(x+1)(x+2)]} / [(3x-6)/(2x²-x-1)] =
(3x+3)/ [(x+1)(x+2)]  · (2x²-x-1)/(3x-6) =
3/(x+2) · (2x²-x-1)/(3x-6)=           
(2x²-x-1)/[(x+2)(x-2)]=
(2x+1)(x-1]/(x²-4)

B) [ 1/(x²-2x) -1/(x²+2x) +2/(x²-4)] / [(2x+6)/(x³-4x)]=
[ x²+2x-(x²-2x)+2x²] / (x la p4 -4x²)  · x(x²-4)/(2x+6)=
(2x²+4x)·x(x²-4) / [x²(x²-4)(2x+6)]=
(2x²+4x) / [x(2x+6)]=
(2x+4)/(2x+6)=(x2)/(x+3).

C) [ 1/(x²-x) -1/(x²+x) +(x+3)/(x²-1)] ·(x³+4x²-5x)/(x²-x-6)=
[x²+x-(x²-x)+x²(x+3)] / [x²(x²-1)] · x(x²+4x-5)/(x²-x-6)=
(x²+x-x²+x+x³+3x²)·x(x+5)(x-1)  /  [x²(x-1)(x+1)(x+2)(x-3)]=
(x³+3x²+2x)(x+5) / [x(x+1)(x+2)(x-3)]=
x(x+1)(x+2)(x+5) / [x(x+1)(x+2)(x-3)]=         (x+5)/(x-3)

D) [1/(3x-2)-4/(3x+2)-(3x-7)/(4-9x²)] ·(3x²+5x+2)/(1-2x)=
{ [3x+2-4(3x-2)] / (9x²-4) -(3x-7)/(4-9x²)} ·(3x+2)(x+1)/(1-2x)=
[(3x+2-12x+8)/(9x²-4) - (3x-7)/(4-9x²)] ·(3x+2)(x+1)/(1-2x)=
[(-9x+10)(3x+2)/(9x²-4) - (3x-7)(2+3x)/(4-9x²)]·(x+1)/(1-2x)=
[(-9x+10)/(3x-2) - (3x-7)/(2-3x)] · (x+1)/(1-2x)=
[(-9x+10)(2-3x) -(3x-7)(3x-2)] / [(2-3x)(3x-2)] ·(x+1)/(1-2x)=
(-18x+27x²+20-30x-9x²+6x+21x-14)/(6x-4-9x²+6x) ·(x+1)/(1-2x)=
(18x²-21x+6)/(-9x²+12x-4) ·(x+1)/(1-2x)=
(3x-2)(6x-3)/(-[3x-2]²) · (x+1)/(1-2x)=
-(6x-3)/(3x-2) · (x+1)/(1-2x)=
-3(1-2x)/(3x-2)·(x+1)/(1-2x)=-3(x+1)/(3x-2)