College Algebra

Question

Answer in interval form. 

(x-5)(x+3)/x≥0 

Answer 1

The given function changes signs at -3, 0 and 5 (solving taking it as an equation: zeros at -3 and 5, undefined at 0).

 

Choose test points in intervals  (-∞,-3], [-3,0), (0,5] and [5,∞). Do not pick the end points as they will result in zeros or undefined.

 

Plug them in the given inequality and check the signs.

 

You will find it to be positive in the intervals [-3,0) U [5,∞)