SOLUTION: Here is another one. Maybe once I get the hang of it I won't have to ask so many questions :) (x^2)/(3x^2-5x-2) - (2x)/(3x+1) x (1)/(x-2) The help is again appreciated. Some

Question 269966: Here is another one. Maybe once I get the hang of it I won't have to ask so many questions :)
(x^2)/(3x^2-5x-2) - (2x)/(3x+1) x (1)/(x-2)
The help is again appreciated. Some day I will have to understand this, I am sure it will be on a test! :)
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
Here is another one. Maybe once I get the hang of it I won't have to ask so many questions :)
(x^2)/(3x^2-5x-2) - (2x)/(3x+1) x (1)/(x-2)
The help is again appreciated. Some day I will have to understand this, I am sure it will be on a test! :)
Using the rule that says (a/b)*(c/d) = (a*c)/(b*d) when we multiply out the expession on the right we then would have:
x^2/(3x^2-5x-2) - (2x*1)/[(3x+1)*(x-2)]
Multiplying out the denominator on the right we have:
x^2/(3x^2-5x-2) - 2x/(3x^2 - 6x + x -2) or
x^2/(3x^2-5x-2) - 2x(3x^2-5x-2)
Notice that each of these expressions has the same denominator so, using the rule that says a/b - c/b = (a-c)/b we have:
(x^2-2x)/(3x^2-5x-2)
Let's factor the numerator and denominator to see if we can simplify this?
[x*(x-2)]/[(3x+1)*(x-2)]
The factor x-2 cancels out so we have:
x/(3x+1)

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