# Rational Function Inequality

• Oct 11th 2009, 05:00 PM
Isimbot
Rational Function Inequality
3x-5

______ -1 is less than or equal to 0

x - 3

Doesn't the -1 change everything? What would be a zero normally, is now a negative one. So should I find the zeros without considering the -1 then add 1 to the zeros and call it good? No, because the multiplication wouldn't work correctly... Please help, and thanks.
• Oct 11th 2009, 05:27 PM
skeeter
Quote:

Originally Posted by Isimbot
3x-5

______ -1 is less than or equal to 0

x - 3

Doesn't the -1 change everything? What would be a zero normally, is now a negative one. So should I find the zeros without considering the -1 then add 1 to the zeros and call it good? No, because the multiplication wouldn't work correctly... Please help, and thanks.

$\displaystyle \frac{3x-5}{x-3} - 1 \le 0$

$\displaystyle \frac{3x-5}{x-3} - \frac{x-3}{x-3} \le 0$

$\displaystyle \frac{2x-2}{x-3} \le 0$

critical values ...

$\displaystyle x = 1$ and $\displaystyle x = 3$

for $\displaystyle x < 1$ ... the inequality is false

for $\displaystyle 1 < x < 3$ ... the inequality is true

for $\displaystyle x > 3$ ... the inequality is false

solution set is $\displaystyle 1 \le x < 3$