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find all values of x such that \(\frac{2x}{x + 2} = -\frac{6}{x + 4}.\)

 Apr 19, 2020
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Multiply both sides by (x+2) * (x+4) or "cross multiply" to get:

\(2x(x+4) = -6(x+2)\)

Expanding out, we get:

\(2x^2+8x = -6x - 12\)

Adding 6x and 12 on both sides of the equation, we then get the quadratic:

\(2x^2 +14x+12 = 0\)

We can then factor this into:

\((2x+2)(x+6) = 0\)

The values for which this is 0 are -1 and -6

 Apr 20, 2020

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