Calculus Question

Question

log(x² + 2x - 3/ x² - 4) - log (x² + 7x + 6/ x + 2)

Answer 1

We first use the log rule:

log a - log b = log(a/b)

to get:

log(x² + 2x - 3/ x² - 4) - log (x² + 7x + 6/ x + 2) = log((x² + 2x - 3/ x² - 4)*((x+2)/(x² + 7x + 6)))

= log((x-3)(x+1)(x+2)/(x+2)(x-2)(x+6)(x+1)) = log((x-3)/(x+6)(x-2))