SOLUTION: solve the equation 1/x-2 - 4/x^2-4 = 5 please help me solve this equation

Question 197269: solve the equation
1/x-2 - 4/x^2-4 = 5
please help me solve this equation

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Ignore the previous post (there is a solution).

Start with the given equation.

Factor the second denominator

Take note that or (these values cause a division by zero)

Simplify

FOIL

Distribute

Combine like terms.

Get everything to one side.

Combine like terms.

Notice we have a quadratic 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, recall that we stated that (this values causes a division by zero). So is NOT a solution.

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

Answer:

So the only solution is
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