Solve $LaTeX: \displaystyle \frac{7}{x - 5}=\frac{4}{x - 9}$ .

The LCD is $LaTeX: \displaystyle \left(x - 9\right) \left(x - 5\right)$ . Multiplying by the LCD to clear the fractions gives $LaTeX: \displaystyle 7 x - 63 = 4 x - 20$ . Isloating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = \frac{43}{3}$ .