Question

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

Answer 1

Answer:

D

Step-by-step explanation:

Consider the inequality

$\dfrac{x^2+4x-12}{x}>0$

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

$\dfrac{(x+6)(x-2)}{x}>0$

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.

Answer 2

Answer:

D

Step-by-step explanation: