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Question
Reduce the following rational expression to its lowest form
`("p"^2 - 3"p" - 40)/(2"p"^3 - 24"p"^2 + 64"p")`
Solution
`("p"^2 - 3"p" - 40)/(2"p"^3 - 24"p"^2 + 64"p")`
p2 – 3p – 40 = (p – 8) (p + 5)
2p3 – 24p2 + 64p = 2p (p2 – 12p + 32)
= 2p (p – 8) (p – 4)
`("p"^2 - 3"p" - 40)/(2"p"^3 - 24"p"^2 + 64"p") = (("p" - 8)("p" + 5))/(2"p"("p" - 8)("p" - 4))`
= `("p" + 5)/(2"p"("p" - 4))`
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