Question 1051852
<pre><b>{{{(x^4(3x-5)^2(x+1)^2)/(x^2-3x+2)>=0}}}

The denominator is the only thing not factored,
so factor it

{{{(x^4(3x-5)^2(x+1)^2)/((x-1)(x-2))>=0}}}

The critical numbers are the zeros of all the factors:

0, {{{5/3}}}, -1, 1, 2

Arrange them in numerical order:

-1, 0, 1, {{{5/3}}}, 2

-1, 0, 1, {{{1&2/3}}}, 2

and put them on a number line:

-----------o----o----o--o-o------
-3   -2   -1    0    1    2    3 

Choose test values less than the least, in between
them, and greater than the greatest:

Test values: -2, -0.5, 0.5, 1.5, 1.9, 3

If the test value gives {{{"">=0}}} when substituted
in the open interval which the test value is in is 
part of the solution; otherwise it's not.

Substituting -2 gives 161.333... which is {{{"">=0}}},
so {{{(matrix(1,3,-infinity,",",1))}}} is part of
the solution.

Substituting -0.5 gives 0.176... which is {{{"">=0}}},
so {{{(matrix(1,3,-1,",",0))}}} is part of
the solution.
  
Substituting 0.5 gives 2.296... which is {{{"">=0}}},
so {{{(matrix(1,3,0,",",1))}}} is part of
the solution.
 
Substituting 1.5 gives -31.64... which is {{{""<0}}},
so {{{(matrix(1,3,1,",",5/3))}}} is NOT part of
the solution.

Substituting 1.9 gives -596.71... which is {{{""<0}}},
so {{{(matrix(1,3,5/3,",",2))}}} is NOT part of
the solution.

Substituting 3 gives 10368 which is {{{"">=0}}},
so {{{(matrix(1,3,1,",",2))}}} is part of
the solution.

The critical numbers from the numerator 0,5/3, and -1
satisfy the given inequality since "equal to 0" is allowed.  
However the critical numbers from the denominator, 1 and 2, 
do not.

Solution set:

{{{matrix(1,3,

(matrix(1,3,-infinity,",",1)),

U,

(matrix(1,3,2,",",infinity))
)}}}

Edwin</pre>