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.
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Answer:
So the solution is
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