Solving rational inequalities and use sign diagram to sketch the graph. image attached for better understanding.

x ∈ (-∞ , -2) ∪ (-1, 1)

Step-by-step explanation:

The expression is already factored. Note that for the polynomial that appears in the numerator there is 1 root:

For the polynomial that appears in the denominator there are 2 roots:

Note that and does not belong to the domain of f(x) because it zeroes the denominator of the function and the division between zero is not defined.

With these three roots we do the study of signs to find out when

Observe the attached image

Note that:

when

when

when

Finally, we have the solution:

x ∈ (-∞ , -2) ∪ (-1, 1)

dilation scale factor 2: starting with δabc, draw the dilation image of the triangle with a center at the origin and a scale factor of two. notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). dilation with scale factor 2, multiply by 2.