Solve $LaTeX: \displaystyle \frac{5}{x - 9}=- \frac{4}{x - 4}$ .

The LCD is $LaTeX: \displaystyle \left(x - 9\right) \left(x - 4\right)$ . Multiplying by the LCD to clear the fractions gives $LaTeX: \displaystyle 5 x - 20 = 36 - 4 x$ . Isloating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = \frac{56}{9}$ .