This week in PreCalc 11 we learned how to multiply and divide rational expressions.

Rational Expressions are fractions whose numerator and denominator are both polynomials and this week we learned how to multiply two rational expressions together. Typically when we multiply two regular fractions together, we multiply the top numbers which turns equals the numerator and multiply the bottom numbers which equals the denominator. Then at the end we simplify the remaining fraction. The same idea goes for multiplying two or more rational expressions together.

Example:

Explanation:

Step 1: completely factor 

Factor all the polynomials present in the rational expressions. All factors should be completely factored.

Step 2: name non permissible values

Typically with regular factors, the denominator can never equal zero. The same concept goes for rational expressions, the denominator can’t equal zero. That is why if there is ever a variable on the denominator it can’t equal any numbers that would make the denominator zero. In this case, if x equals 1, -1, 9, -9, 0 then the denominator would equal zero so that’s why we must put that x cannot equal these numbers.

Step 3: simplify

To simplify, cross out any factors that are the same on the top and the bottom.

Final Answer:

The final answer will equal all the numbers that remain on top multiplied together to equal the numerator, and the same goes for the denominator.