Solve $LaTeX: \displaystyle \frac{7}{x + 6}=\frac{9}{x + 9}$ .

The LCD is $LaTeX: \displaystyle \left(x + 6\right) \left(x + 9\right)$ . Multiplying by the LCD to clear the fractions gives $LaTeX: \displaystyle 7 x + 63 = 9 x + 54$ . Isloating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = \frac{9}{2}$ .