SOLUTION: solve (x+1/x^2-4)=(3/x+2)+(5/3x-6)
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Question 229895: solve (x+1/x^2-4)=(3/x+2)+(5/3x-6)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Solve:
At some point we will need to eliminate the fractions. To me, it is easiest to eliminate them early. Fractions in an equation can be eliminated if you multiply both sides of the equation by the Lowest Common Denominator (LCD) of all the fractions. (Normally the LCD is used for adding and subtracting fractions. But it can be used for this, too.) To find the LCD we need to factor the denominators:
Now that we can see the factors of the different denominators, we can figure out the LCD. The LCD is the product of all the different factors in the denominators:
LCD: (x+2)*(x-2)*3
Note that the (x-2), even though it occurs in two denoinators, is only used once in the LCD. Now we will multiply both sides by the LCD:
On the right side we need to use the Distributive Property:
As we multiply we will see a lot of canceling:
leaving
We now have a pretty simple equation to solve:
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