+128475 29) factor top / bottom
( x + 2) ( x - 2)
___________
-3 ( x + 3)
"Holes" will only be created when we can "cancel" factors
Here....nothing "cancels" ....so......no "holes"
We will have a vertical asymptote at x = -3 and something known as a "slant asymptote"
The latter will occur because we have a greater degree polynomial divided by a lesser degree polynomial
30) factor top / bottom
(x + 3) ( x - 2) (x + 3) ( x - 2)
______________ = _____________
3 ( x^2 + 4x + 3) 3(x + 3) ( x + 1)
Note that the "x + 3" factor will "cancel"
So.....to find the "hole".....set x + 3 = 0 and solve for x......and we have
x + 3 = 0
x = -3
So.....we have a hole at x = -3
See the graph, here : https://www.desmos.com/calculator/oshh1sofob
RP.....If you hold down the left button on your mouse/laptop and drag the cursor along the curve...note....at x = -3.....you will see "undefined" = (a "hole" here )
