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

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Question 270261:
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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