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Find all values of \(x\) such that \(\dfrac{x}{x+4} = -\dfrac{9}{x+3}\). If you find more than one value, then list your solutions in increasing order, separated by commas.

Logic  Sep 14, 2018
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Solve for x:
x/(x + 4) = -9/(x + 3)

Cross multiply:
x (x + 3) = -9 (x + 4)

Expand out terms of the left hand side:
x^2 + 3 x = -9 (x + 4)

Expand out terms of the right hand side:
x^2 + 3 x = -9 x - 36

Add 9 x + 36 to both sides:
x^2 + 12 x + 36 = 0

Write the left hand side as a square:
(x + 6)^2 = 0

Take the square root of both sides:
x + 6 = 0

Subtract 6 from both sides:
x = -6

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