College Algebra
posted by Liz on .
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solve the Polynomial inequality and express the solution in set notation.
(3p2p^2)/(4p^2)<(3+p)/(2p)

You want
(3p2p^2)/(4p^2)  (3+p)/(2p) < 0
p(32p)/(2p)(2+p)  (3+p)(2+p)/(2p)(2+p) < 0
[p(32p)  (3+p)(2+p)]/(2p)(2+p) < 0
(3p  2p^2  p^2  5p  6)/(2p)(2+p) < 0
(3p^2 + 2p + 6)/(2p)(2+p) > 0
The numerator is always positive.
So, we want the region where 4p^2 is positive.
That is, 2 < p < 2
Just to check, graph the two functions, and you'll see that this is the case. 
Factor the polynomials by pulling out the GCF
6r^2+12r15 
Sorry, I posted in the wrong place :(