SOLUTION: x/x+1 + 5/x = 1/x^2+x

Question 200942: x/x+1 + 5/x = 1/x^2+x
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Factor the last denominator

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

Simplify

Distribute

Multiply

Subtract 1 from both sides.

Combine like terms.

Notice that the quadratic is 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

Subtract from 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 , this means that the only solution is

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Answer:

So the solution is
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