+1206 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.
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
