Expert: Ahmed Salami - 2/1/2010

Question
Hello, I am studying for a test i have next week and i am stuck on this question i need to give the values of x that satisfy the following equation.

x^2-3x+2/ x^2-6x+9  is greater then or equal to 0.

Thank you in advance.

-Max

Answer
Hi Max,
We have the inequality
(x² - 3x + 2)/(x² - 6x + 9) >= 0
factorizing,
(x-2)(x-1)/(x-3)² >= 0
In inequalities we are free to multiply both sides by a positive expression while preserving the sign. (x-3)² is always positive.
And so,
(x-2)(x-1) >= 0.(x-3)²
(x-2)(x-1) >= 0
We know that (x-2)(x-1) is zero when x = 1 or 2 and this points divide the x axis into three regions; x<1, 1<x<2 and x>2
A point in each region is taken and tested in the inequality to determine the applicable intervals. We end up with a solution of x <= 1 and x >= 2

You can always get back to me.

Regards.