+144
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.
+343 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!
+343 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!
