SOLUTION: Problem with more than one solution. Question: x/3 = 4/x+1 4/x+1 - x/3 = 0 3(x+1)4/x+1 - x/3 3(x+1) = 0 3(4) - x(x+1) = 0 12 - x^2

SOLUTION: Problem with more than one solution. Question: x/3 = 4/x+1 4/x+1 - x/3 = 0 3(x+1)4/x+1 - x/3 3(x+1) = 0 3(4) - x(x+1) = 0 12 - x^2 - x

Question 194424: Problem with more than one solution.
Question: x/3 = 4/x+1
4/x+1 - x/3 = 0
3(x+1)4/x+1 - x/3 3(x+1) = 0
3(4) - x(x+1) = 0
12 - x^2 - x = 0
12 - x^3 = 0
Did I go wrong or where do I go from here? Thank You.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You made a mistake in assuming that which is NOT true. You CANNOT combine variables of different powers.

What you need to do is solve

Start with the given equation.

Rearrange the terms.

Multiply EVERY term by -1 to make the leading coefficient positive.

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 solutions are or

To verify the solutions, simply plug them back into