SOLUTION: Solve the inequality {{{x/(x-4)

SOLUTION: Solve the inequality {{{x/(x-4) - (x-1)/(x+3) <= 1}}}.

Question 1183643: Solve the inequality
.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
After combining the terms on the left-hand side of the inequality, we get
.

<===> .
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 ~ 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 (, -3), (-3, -0.815), [-0.815, 4), (4, -9,815), and [9.815, ).

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

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