3а)
{ (x+5)/(x-4) -(x+3)/(x-1)> 0; 3x -7>x+1.⇔
{ ((x+5)(x-1) -(x+3)(x-4))/(x-1)*(x-4 )> 0; 3x -x >7+1.⇔
{ (x²+4x-5 -x²+x+12)/(x-1)*(x-4 )> 0; 2x >8.⇔
{ 5(x+1,4)/(x-1)*(x-4 )> 0; x >4.⇒ x >4.
ответ: x∈ (4 ;∞) .
- + - +
------ (-1,4) //////// (1) ------ (4) //////////
----------------------------------(4) /////////
* * * * * * * * * * * * * * * * * * * * *
3б)
{(6x-1)/(x+4) -2 ≤0 ; 5(x-8)>6x⇔{(6x-1 -2x -8)/(x+4) ≤0 ; 5x-40>6x.
{4(x-9/4)/(x+4) ≤0 ; - 40>x. ⇔{x ∈(-4; 9/4]; x< -40⇒ x ∈ ∅.
ответ: x ∈ ∅ .
+ - +
----------------- (-4)//////////[ 9/4] -------
//////// (-40) ------------------------------