Solve $LaTeX: \displaystyle \frac{5}{x + 3}=\frac{4}{x - 5}$ .

The LCD is $LaTeX: \displaystyle \left(x - 5\right) \left(x + 3\right)$ . Multiplying by the LCD to clear the fractions gives $LaTeX: \displaystyle 5 x - 25 = 4 x + 12$ . Isloating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 37$ .