Last week we learned about Rational Expression, aka all real values of the variable except for those values that make the denominator zero. AKA2: In x/y, how to make sure y is not 0.
In particular, we learned about the how to make sure the denominator not equal 0 with something called non-permissible(the numbers one can’t use, or the denominator will equal zero and the expression will no longer be Rational.)
Outside of non-permissible values, we also learned how to simplify and/or multiple, divide Rational Expressions. But due to the fact, a Rational Expression or any real number, in this case, is a fraction, all to be done is to follow the law of dividing and multiplying of the fractions. AKA: why diving, multiply by it’s reciprocal. and why multiplying just multiply the numerator with the numerator and the denominator and denominator, but just keep in mind that in any rational expression the denominator can’t be 0, so there may be non-permissible as well. And as it’s an expression, all you can do is to simplify it.
In a fraction, when denominator equals the numerator, the number equals 1. EX: 8/8=1
So in an equation such as 3x.8(x-3)/2(x-3).9x^2. It might be helpful to use factoring to find the common thing that can cancel out to 1, like how (x-3) and 3x in this case. So after finding the common terms. they will just cancel out to 1, and in this case, 3x and 9x^2,(x-3)and (x-3) cancels out. and leaves you with 8/2.3x=8/6x=4/3x and don’t forget about the non-permissible, and remember you have to find them in the original equation, as they will be lost when you simplify the equation. In this case(x-3)can’t be 0, therefore x not equal 3, and 9x^2 can’t be 0, therefore x can’t equal 0.