I want to play with this one, too
[x^2 -7x + 6] / [x^2 - 8x + 12] > 0 factor top and bottom
[(x - 6) (x - 1)] / [ (x - 6) ( x - 2) ] > 0 Note that this simplifies to :
(x - 1) / ( (x - 2) > 0 however, we have to be aware that our grpah will have a "hole" at x = 6
The intervals of interest are (-∞, 1) (1, 2) (2, ∞ )
If you check, the two "outside" intervals make the equation the original eqaution true....again, we have to be aware that the last interval will have the "hole" where x = 6......here's the graph.....
https://www.desmos.com/calculator/yyh7iwefu0
Even though, the "hole" doesn't show up on the graph, you can hold down the left button on your mouse and drag along the curve....at x =6, you will see that Desmos displays "undefined" at that point...!!!
So ......the "true" answer to the problem is (-∞, 1) U (2, 6) U (6, ∞ )
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Interest Posts:
1) Number Puzzle No answer
2) Ratio question Thanks CPhill and Heureka
3) Inequalities with holes Melody
4) Max and min with absolute value in the equation. Thanks CPhill and Heureka.
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