Question

Which graph shows the solution set of x^2+4x-12/x>0?

Answer 1

D

Explanation:

Answer 2

D

Explanation:

Consider the inequality

`(x^2+4x-12)/(x)>0`

First, factor the numerator:

`x^2+4x-12=x^2+6x-2x-12=x(x+6)-2(x+6)=(x+6)(x-2)`

Now, the inequality is

`((x+6)(x-2))/(x)>0`

The equivalent inequality is

`x(x+6)(x-2)>0`

On the number line plot doted points -6, 0 and 2 and put signs +, -, +, - from the right to the left. Intervals with + signs are the solution of the inequality:

`x\in(-6,0)\cup(2,\infty)`

that is represented by D number line.