Solve $LaTeX: \displaystyle \frac{10}{x + 4}=- \frac{9}{x - 8}$ .

The LCD is $LaTeX: \displaystyle \left(x - 8\right) \left(x + 4\right)$ . Multiplying by the LCD to clear the fractions gives $LaTeX: \displaystyle 10 x - 80 = - 9 x - 36$ . Isloating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = \frac{44}{19}$ .