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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.

HelpPLZ  Oct 18, 2018

Best Answer 

 #1
avatar+307 
+2

First of all we eill find domain of equation. x ≠ -4, x ≠  -3 because if x = -4,-3 we will have in denominator 0 

After this we start

\((x+3)(x) = -(x+4)(9) <=>\)

\(<=> x^2+3x = -9x -36 <=> \)

\(<=> x^2 + 12x + 36 = 0 <=> \)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a} \)

x= -12/2 = -6 and

\(-6≠ -3,-6≠ -4 \) 

so \(x=-6\) is the answer.

Hope it helps! 

Dimitristhym  Oct 18, 2018
 #1
avatar+307 
+2
Best Answer

First of all we eill find domain of equation. x ≠ -4, x ≠  -3 because if x = -4,-3 we will have in denominator 0 

After this we start

\((x+3)(x) = -(x+4)(9) <=>\)

\(<=> x^2+3x = -9x -36 <=> \)

\(<=> x^2 + 12x + 36 = 0 <=> \)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a} \)

x= -12/2 = -6 and

\(-6≠ -3,-6≠ -4 \) 

so \(x=-6\) is the answer.

Hope it helps! 

Dimitristhym  Oct 18, 2018

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