vault backup: 2024-01-17 10:14:33

education/math/Rational Inequalities.md

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+## Basic Form
 $$ \frac{x+3}{x-4} < 0 $$
-1. Look at the bottom, solve for zero. When the bottom equals zero, 
+
+1. Draw a number line. 
+2. Look at the bottom of the fraction $x - 4$, solve for x($x = 4$ ). When the bottom equals zero, put an empty circle on the line to mark a hole, because you cannot divide by 0.
+3. Look at the top, solve for zero, and put another point on the line. If it's $\le 0$, this point is filled in, otherwise it's another hole. Now check each "section" along the line by plugging in an arbitrary value to see if the result evaluates to less than zero.
+
+$$ \frac{(x+1)^2}()