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

The LCD is $LaTeX: \displaystyle \left(x - 4\right) \left(x + 10\right)$ . Multiplying by the LCD to clear the fractions gives $LaTeX: \displaystyle 4 x - 16 = - 8 x - 80$ . Isloating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = - \frac{16}{3}$ .