Solve $LaTeX: \displaystyle \frac{4}{x - 5}=\frac{8}{x - 10}$ .

The LCD is $LaTeX: \displaystyle \left(x - 10\right) \left(x - 5\right)$ . Multiplying by the LCD to clear the fractions gives $LaTeX: \displaystyle 4 x - 40 = 8 x - 40$ . Isloating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 0$ .