Rational expression

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Problem 4
Find the LCD for the expressions below and convert each rational expression into an equivalent rational expression with the LCD as the denominator.

2 p2 + 7p -15= 2 p2 + 10 p- 3 p - 15 = 2p (p+ 5) -3 (p-5) = (2p-3) (p+5)
2 p2 - 11p +12 = 2 p2 - 8 p- 3 p + 12 = 2p (p- 4) -3 (p-4) = (2p-3) (p-4)
p2 + p -20 = p2 + 5 p- 4 p - 20 = p (p+ 5) -4 (p+4) = (p-4) (p+5)

Thus
2 p2 + 7p -15= (2p-3) (p+5)
2 p2 - 11p +12 = (2p-3) (p-4)
p2 + p -20 = (p-4) (p+5)

LCD of denominators= (2p-3) (p+5) (p-4)

Thus

Instead of writing (2p-3) (p+5) (p-4) in the denominator we can also write

2 p3 - p2 -43 p + 60

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