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Identify the holes

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Not sure what the holes are Nov 14, 2018

#1
+2

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 )   Nov 14, 2018
#2
+1

tysm!

RainbowPanda  Nov 14, 2018