SOLUTION: SOLVE THE EQUATION 2/x-2+x/x+2=x+6/x^2-4

Question 170414: SOLVE THE EQUATION
2/x-2+x/x+2=x+6/x^2-4
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 on both sides by the LCD . Doing this will eliminate all of the fractions.

Multiply and simplify

Distribute.

Subtract x from both sides. Subtract 6 from 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 answers are or

However, if you plug in , you'll get a division by zero. So is not an answer (since is not even in the domain).

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Answer:

So the solution is

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