# How do you solve # 5 /(x^2 + 4x) = 3 / x - 2/(x + 4)#?

Let's write all the fractions with the same denominator :

Now, let's put all the fractions on the left :

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To solve the equation 5/(x^2 + 4x) = 3/x - 2/(x + 4), we can start by finding a common denominator for the fractions on the right side. The common denominator is x(x + 4).

Multiplying both sides of the equation by x(x + 4), we get:

5(x)(x + 4) = 3(x + 4) - 2(x)

Expanding and simplifying the equation:

5x^2 + 20x = 3x + 12 - 2x

Combining like terms:

5x^2 + 20x = x + 12

Moving all terms to one side of the equation:

5x^2 + 20x - x - 12 = 0

Simplifying further:

5x^2 + 19x - 12 = 0

To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, factoring is the most efficient method.

Factoring the quadratic equation:

(5x - 3)(x + 4) = 0

Setting each factor equal to zero:

5x - 3 = 0 or x + 4 = 0

Solving for x in each equation:

5x = 3 or x = -4

Dividing both sides by 5:

x = 3/5 or x = -4

Therefore, the solutions to the equation 5/(x^2 + 4x) = 3/x - 2/(x + 4) are x = 3/5 and x = -4.

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