On which interval is the function increasing

(-1,0) and (1, infinity)

(-1,0) U (1, infinity)

Step-by-step explanation:

The function is said to increase, when the y-values it adopts (as seen from its graph) give larger and larger values as you read the graph from left to right (like when you read the newspaper). Therefore, the function is said to increase,when you see the graph going up.

You can see two regions of the graph "going up" as you move your eyes following the trace of the function from left to right in the sections highlighted in the attached image.

Normally you are asked what are the intervals (or sections of the Domain of the function) where such happens. Recall that the domain is the set of x-values over which the function is defined. Therefore you are asked to give the  subset of x-values (on the horizontal axis) for which the increase takes place.

As you see in the image (also highlighted) those sections are the x-values in between -1 and 0, and also the values from 1 towards positive infinity.

When describing such multiple subsets in Math, we normally use the symbol "U" to denote the union of two sets:

(-1,0) U (1, infinity)

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.