SOLUTION: Need help with solving this equation. 2=(x+3)/(x+2)+5/(x^2-x-6)

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Question 171794: Need help with solving this equation.
2=(x+3)/(x+2)+5/(x^2-x-6)

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation.


Factor to get


Take note that the LCD is



Multiply EVERY term by the LCD to clear out the fractions.


Multiply and simplify


FOIL


Distribute


Combine like terms.


Subtract from both sides. Add 4 to both sides.


Combine like terms.



Notice we have a quadratic equation in the form of where , , and


Let's use the quadratic formula to solve for x


Start with the quadratic formula


Plug in , , and


Negate to get .


Square to get .


Multiply to get


Rewrite as


Add to to get


Multiply and to get .


Take the square root of to get .


or Break up the expression.


or Combine like terms.


or Simplify.


So the possible solutions are or

However, if you plug in back into the original equation, a division by zero will occur.

So is NOT a solution.


==============================================================================

Answer:


So the solution is

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