Simplifying rational expressions

Thinking back to when you were dealing with whole number fractions , one of the first things you did was simplify them: You "cancelled off" factors which were in common between the numerator and denominator. You could do this because dividing any number by itself gives you just "1", and you can ignore factors of "1".

Using the same reasoning and methods, let's simplify some rational expression

SIMPLIFY THE EXPRESSION

2X/X²

When you dealt with fractions, you knew that the fraction could have any whole numbers for the numerator and denominator, as long as you didn't try to divide by zero. When dealing with rational expressions, you will often need to evaluate the expression, and it can be useful to know which values would cause division by zero, so you can avoid these x-values. So probably the first thing you'll do with rational expressions is find their domains.

 Find the domain of 3/x

The domain is all values that x is allowed to be. Since I can't divide by zero (division by zero isn't allowed), I need to find all values of x that would cause division by zero. The domain will then be all otherx-values. When is this denominator equal to zero? When x = 0.

Then the domain is "all x not equal to zero".