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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.

 Apr 24, 2019
 #1
avatar+18346 
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multiply both sides by x+4

to get

x = -9(x+4) / (x+3)     Multiply both sides by x + 3 to get

 

x (x+3) = -9 (x+4)    expand

x^2 + 3x = - 9x - 36

x^2 + 12x + 36 = 0    factor

(x+6)(x+6) = 0           two roots   at   x = -6

 Apr 24, 2019
 #2
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I think part of your awsnere did not render.  I just have blank spaces

 Apr 25, 2019

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