algebra problem

Question

((x^2+4)(x-3)^3/(x+5)(x-7))/< 0

Answer 1

When you have factored rational expression, it is best to use "interval" method.

x^2+4 is always positive, so you could disregard it for our purposes

Put special points (where each factor turns 0) - +3, -5, +7 on the numeric line and note the sign of the expression on each interval.

(-∞, -5) - negative

(-5, 3) - positive

(3,7) - negative

(7, ∞) - positive

Here you go. The answer is (-∞, -5) ∪ (3, 7)

If you need a lesson on interval method - please let me know. Thanks