Solve $LaTeX: \displaystyle \frac{6}{x - 1}=\frac{1}{x + 7}$ .

The LCD is $LaTeX: \displaystyle \left(x - 1\right) \left(x + 7\right)$ . Multiplying by the LCD to clear the fractions gives $LaTeX: \displaystyle 6 x + 42 = x - 1$ . Isloating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = - \frac{43}{5}$ .