SOLUTION: Please help me with this problem {{{y= (6x^2+x-2)/(3x^2+17x+10)}}} I need to describe the vertical asymptots and holes for the graphy of the rational function

Question 139068This question is from textbook Prentice Hall Mathematics Algebra 2
: Please help me with this problem
I need to describe the vertical asymptots and holes for the graphy of the rational function This question is from textbook Prentice Hall Mathematics Algebra 2

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
y= (6x^2+x-2)/(3x^2+17x+10)
Factor where you can:
6x^2 + x -2 = 6x^2+4x-3x-2 = 2x(3x+2)-(3x+2) = (3x+2)(2x-1)
--------
3x^2 + 17x + 10 = 3x^2 + 15x + 2x + 10 = 3x(x+5) + 2(x+5)= (x+5)(3x+2)
------------
Now the problem can be written as:
y= [(3x+2)(2x-1)] / [(x+5)(3x+2)]
----------------
Because numerator and denominator have a factor of 3x+2 there is a hole at
x=-2/3
----------------
There is a vertical asymptote at x=-5
=============================
Cheers,
Stan H.
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