Chapter 4 - Exponential and Logarithmic Functions - Section 4.5 Properties of Logarithms - 4.5 Assess Your Understanding - Page 331: 64

$log\frac{(x+3)(x-1)}{(x-2)(x+6)(x+1)} ,x\ne-2$

$log\frac{x^2+2x-3}{x^2-4}-log\frac{x^2+7x+6}{x+2}=log\frac{(x+3)(x-1)}{(x+2)(x-2)}-log\frac{(x+6)(x+1)}{x+2}=log[\frac{(x+3)(x-1)}{(x+2)(x-2)}\times\frac{x+2}{(x+6)(x+1)}]=log\frac{(x+3)(x-1)}{(x-2)(x+6)(x+1)} ,x\ne-2$