Question 1183643
After combining the terms on the left-hand side of the inequality, we get

{{{(x(x+3) - (x-4)(x-1))/((x-4)(x+3)) = (8x-4)/((x-4)(x+3)) <= 1}}}.


<===> {{{0 <= 1 -  (8x-4)/((x-4)(x+3))  = (x^2 - 9x -8)/((x-4)(x+3))}}}.

The critical values of the right-hand side are the x values in which the numerator and denominator are equal to 0.  


The roots of the top are {{{x = (-(-9) +- sqrt( (-9)^2-4*1*-8 ))/2  = (9 +- sqrt(113))/2}}} ~ 9.815, -0.815.  The roots of the bottom are clearly 4 and -3.


The real number line is thus partitioned into five subintervals, namely ({{{-infinity}}}, -3), (-3, -0.815), [-0.815, 4), (4, -9,815), and [9.815, {{{-infinity}}}).


Get a convenient test point from each subinterval, and then substitute into the expression  {{{(x^2 - 9x -8)/((x-4)(x+3))}}}, keeping in mind that we need this 
expression to be non-negative after the substitution. From this we get the general solution  ({{{-infinity}}}, -3) U [-0.815, 4) U [9.815, {{{infinity}}}).