How do you solve (x-4)/(x-3)>0?

1 Answer
Alan P.
Sep 8, 2016

x in {(-oo,3),(4,+oo)}

Explanation:

The "critical" values for x are obviously 3 and 4.

Create a chart for the implied ranges of x:
{: (, " | ",x < 3, " | ",x = 3, " | ", 3 < x < 4, " | ", x=4, " | ",x > 4), ((x-4)/(x-3), " | ",>0, " | ","undefined", " | ",< 0, " | ",=0, " | ",>0) :}

We can see that (x-4)/(x-3) > 0 when x < 3 and when x > 4

Here's a graph of (x-4)/(x-3) that might help verify this result:
graph{(x-4)/(x-3) [-2.05, 10.434, -2.5, 3.74]}

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