Describe the mathematic process of canceling like factors when working with rational expressions... Demonstrate this with an example
I googled,
"simplifying rational expressions"
this is the first page that came up
http://www.purplemath.com/modules/rtnldefs2.htm
The process of canceling like factors in rational expressions involves simplifying the expression by dividing both the numerator and denominator by their common factors. Here's a step-by-step guide on how to do it:
Step 1: Factorize the numerator and denominator.
- Express both the numerator and denominator as products of prime factors.
Step 2: Identify the common factors.
- Look for the factors that are present in both the numerator and denominator.
Step 3: Cancel out the common factors.
- Divide both the numerator and denominator by their common factors.
Step 4: Simplify the expression.
- Rewrite the reduced fraction as the simplified expression.
Now, let's demonstrate this process with an example:
Example: Simplify the expression (6x^2 - 9x) / (3x)
Step 1: Factorize the numerator and denominator.
- The numerator can be factored as (3x)(2x - 3).
- The denominator doesn't require any further factoring as it is already in its simplest form.
Step 2: Identify the common factors.
- In this example, the common factor is 3x.
Step 3: Cancel out the common factors.
- Divide the numerator and denominator by 3x.
- (3x)(2x - 3) / (3x) becomes (2x - 3).
Step 4: Simplify the expression.
- The simplified expression is (2x - 3).
Therefore, by canceling the common factor of 3x, the rational expression (6x^2 - 9x) / (3x) simplifies to (2x - 3).