Question

Hello! I need some help with this homework question posted below. Q22

Answer 1

`\begin{gathered} (-\infty,-4)\cup(7,\infty) \\ \end{gathered}`

Step-by-step explanation

`(x+4)/(x-7)>0`

Step 1

Multiply both sides by (x-7)

`\begin{gathered} (x+4)/(x-7)>0 \\ (x+4)/(x-7)\cdot(x-7)>0(x-7) \\ x+4>0 \\ \text{subtract 4 in both sides} \\ x+4-4>0-4 \\ x>-4 \end{gathered}`

Check possible critical points.

x=-4

`\begin{gathered} (x+4)/(x-7)>0 \\ (-4+4)/(-4-7)>0 \\ (0)/(-11)>0 \\ 0>0 \end{gathered}`

so, test each interval for a positive or negative result, the divide ths igns

we need a result greater than zero ( so a positive number)

therefore, the answer is

`\begin{gathered} (-\infty,-4)\cup(7,\infty) \\ \end{gathered}`

I hope this helps you