Solve $LaTeX: \displaystyle \frac{4}{x - 7}=- \frac{6}{x + 10}$ .

The LCD is $LaTeX: \displaystyle \left(x - 7\right) \left(x + 10\right)$ . Multiplying by the LCD to clear the fractions gives $LaTeX: \displaystyle 4 x + 40 = 42 - 6 x$ . Isloating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = \frac{1}{5}$ .