Question

I need help on how to solve this type of problem please.

29.)Solve the inequality and express the solution in terms of intervals whenever possible.

1/(x-2) ≥ 3/(x+1)


THE ANSWER IS: ( -∞,-1 ) U ( 2,(7/2) ]

Answer 1

1/(x-2) - 3/(x+1) ≥ 0

So we have critical values at x = -1 and x = 2

test for any value x < -1, e.g. x = 10
is 1/-12 ≥ 3/-9 ? YES
test for any value between -1 and 2, say x = 1
is 1/-1 ≥ 3/2 ? NO
test for any value x > 2, say x = 5
is 1/3 > 3/6 ? YES

so solution is
x < -1 OR x > 7/2

suggestion:
enter 1/(x-2) - 3/(x+1)
into "first graph" of
http://rechneronline.de/function-graphs/

to see where the graph is above the x-axis.