SOLUTION: Please help me solve this equation: 2+ 8/x-5=x+5/x^2-25

Question 195562This question is from textbook McDougal Littell Algebra 1
: Please help me solve this equation: 2+ 8/x-5=x+5/x^2-25 This question is from textbook McDougal Littell Algebra 1

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

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

Multiply every term on both sides by the LCD . Doing this will eliminate all of the fractions.

FOIL

Distribute

Get all terms to the left side.

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

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, recall that we stated earlier that (since it causes a division by zero). So is NOT a solution.

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Answer:

So the only solution is

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