Can anyone help me with my homework to show my work to my answers^

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Ответ:

Hhyyuu

05.08.2021

Mathematics

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.

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