Question

solve for all values of x.\\(\frac{x + 6}{x + 4} = \frac{-9}{x}\\)\
answer attempt 1 out of 2\
additional solution no solution\
x =

Explanation:

Step1: Cross-multiply to eliminate fractions

$x(x + 6) = -9(x + 4)$

Step2: Expand both sides

$x^2 + 6x = -9x - 36$

Step3: Bring all terms to left side

$x^2 + 6x + 9x + 36 = 0$
$x^2 + 15x + 36 = 0$

Step4: Factor the quadratic equation

$(x + 3)(x + 12) = 0$

Step5: Solve for x

Set each factor equal to 0:
$x + 3 = 0$ or $x + 12 = 0$

Step6: Verify no undefined values

Check that $x
eq 0$ and $x
eq -4$; both solutions are valid.

Answer:

$x = -3$, $x = -12$