Posted by **Alex** on Sunday, August 12, 2012 at 10:21pm.

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) ]

- Math -
**Reiny**, Monday, August 13, 2012 at 9:43am
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.

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