# How do you solve (t-3)/(t+6)>0 using a sign chart?

Feb 25, 2018

#### Answer:

Solution: $t < - 6 \mathmr{and} t > 3$ In interval notation:
$t | \left(- \infty , - 6\right) \cup \left(3 , \infty\right)$

#### Explanation:

 (t-3)/(t+6)>0 ; t != -6 as the function is undefined at $t = - 6$

Critical points are $t = 3 \mathmr{and} t = - 6$

Sign chart:

When $t < - 6$ sign of $f \left(t\right)$ is (-)/(-)=(+) ; >0

When $- 6 < t < 3$ sign of $f \left(t\right)$ is (-)/(+)=(-) ; <0

When $t > 3$ sign of $f \left(t\right)$ is (+)/(+)=(+) ; >0

Solution: $t < - 6 \mathmr{and} t > 3$ . In interval notation:

$t | \left(- \infty , - 6\right) \cup \left(3 , \infty\right)$