SOLUTION: {{{x/(2x+2)+1/4=-1/(x+2)}}}

Question 270261:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Factor the first denominator.

Take note that the LCD is

Multiply EVERY term by the LCD to eliminate the fractions.

Simplify.

Rearrange the terms.

Multiply.

Distribute.

FOIL.

Get every term to one side.

Combine like terms.

Now let's use the quadratic formula to solve

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=3, b=11, and c=6

Square 11 to get 121

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 3 to get 6

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator

Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator

Divide

So another answer is

So our solutions are:

or

So the solutions to the equation are

or