SOLUTION: Use table of sings to solve inequality: {{{ (x+5)^2(8-x)/(x^2-16) }}} less than or equal to 0 Write solution in interval form. Please explain how these are solved, I nee

Algebra ->  Finance -> SOLUTION: Use table of sings to solve inequality: {{{ (x+5)^2(8-x)/(x^2-16) }}} less than or equal to 0 Write solution in interval form. Please explain how these are solved, I nee      Log On


   

Question 907224: Use table of sings to solve inequality:
++%28x%2B5%29%5E2%288-x%29%2F%28x%5E2-16%29+++ less than or equal to 0

Write solution in interval form. Please explain how these are solved, I need help understanding.
Thank you
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Identify all the critical values of x. Values giving roots (zeros) or asymptotes are the critical values.

Critical values for your expression are -5,-4,4, 8. Check the sign of your expression in the FIVE intervals which these critical points make.

Think of your expression this way:
%28x%2B5%29%5E2%288-x%29%2F%28%28x-4%29%28x%2B4%29%29


Pick ANY value in each interval and test it to find if the rational expression is or is not LESS THAN OR EQUAL TO ZERO. Do not ignore the actual ZEROS of the function because those will be included with your final solution.

(More was here but removed)