Solve $LaTeX: \displaystyle \frac{7}{x + 10}=\frac{4}{x - 7}$ .

The LCD is $LaTeX: \displaystyle \left(x - 7\right) \left(x + 10\right)$ . Multiplying by the LCD to clear the fractions gives $LaTeX: \displaystyle 7 x - 49 = 4 x + 40$ . Isloating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = \frac{89}{3}$ .