Week 14 in Precalc 11

This week in math we learned how to multiply and divide rational expressions. A rational expression is a quotient of two polynomials, so it’ll look like a fraction but with variables. When it comes to multiplying, there are a few simple steps you need to follow.

First, find the non-permissible values. Non-permissible values are variables on the bottom that can’t be a certain number because it would make the denominator equal 0. As we know, you can’t divide by a negative. For example, if the denominator of a rational expression was 2x, then x≠0, because 2×0=0. These will get more complicated as you go along, so it is important to know how to find them. The next step is to simplify, this means factoring the expressions if applicable and then cancelling out numbers and variables when they match or can go into each other. Remember, you can only simplify an expression if one is on the top and the other is on the bottom and if an expression is in brackets, then you have to take the whole thing, not just one part of it. Now, you may want to check if there are any non-permissible values you missed here. Next, you go across and multiply just as you would with regular fractions. But, remember exponent rules, when you multiply the coefficient, you add the exponents. There is your answer! Be sure to check again if there are any more non-permissible values here.

With dividing, you first have to find the non-permissible values. Then you can reciprocate the rational expression you are dividing by, just as you would with regular fractions. Now it is a multiplication question, so you can treat it just as you would with one. Refer to my multiplication steps from here. I’ve included an example below of a multiplication and division question to help visually picture these steps. 