solve the inequality. x^2 (x+6) over (x+6)(x+2) is less than or equal to zero?

Question

express the answer in intervals. ***intervals as in inf and cup signs**

Answer 1

(x+6) cancel top & bottom

x^2 (x+6) / (x+6)(x+2) > 0
=> x^2/(x+2) > 0
X both sides by (x+2)^2

etc

Answer 2

You can cancel x + 6 from num. and denom.,if x NE -6. Then your inequality is x^2/(x+2) <= 0. The numerator is always >= 0, so the inequality is <= 0 if and only if the denom. <= 0, which happens for x <= -2. Now remmember that x NE -6, and if x = 0, the original expression = 0, so the solution is x in (-inf,-6) U (-6,-2] U {0}.