SOLUTION: 3) Division and simplify as much as possible

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Question 88245: 3)
Division and simplify as much as possible

Answer by malakumar_kos@yahoo.com(315) (Show Source):
You can put this solution on YOUR website!
[(3x^2 + 14x + 15)/(3x^2 + 8x + 5)]/[(x^2 - x - 12)/(-3x^2 + 9x + 12)]
Factorise each expressions given and then simplify
3x^2+14x+15 = 3x^2+9x+5x+15 = 3x(x+3)+5(x+3) = (x+3).(3x+5)
3x^2+8x+5 = 3x^2+3x+5x+5 = 3x(x+1)+5(x+1) = (x+1).(3x+5)
x^2-x-12 = x^2-4x+3x-12 = x(x-4)+3(x-4) = (x-4).(x+3)
-3x^2+9x+12 = -3x^2+12x-3x+12 = -3x(x-4)-3(x-4) = (x-4).(-3x-3)
substituting the values we get
(x+3).(3x+5)/(x+1).(3x+5) = (x+3)/(x+1)
(x-4).(x+3)/(x-4).(-3x-3) = (x+3)/(x-4)
(x+3)/(x+1)divided by (x+3)/(x-4)
=(x+3).(x-4)/(x+3).(x+1)
= (x-4)/(x+1)