This week in pre calc 11, we learned about how to solve rational expressions, which specifically are fractions with variables. This week we mainly focused on multiplying and dividing rational expressions, which is what I will cover here. Another very important thing we learned is non-permissible values that x or any variable cannot be in that equation.
Here is a few examples of what rational expressions would look like:
These expressions cannot contain square roots or variable exponents.
A limitation, the domain, or values that the expression cannot be specified by are all examples of non-permissible values. This indicates that some integers, when substituted for x, result in a denominator of zero. The equation can still be simplified when the numerator is zero. This is not feasible when the bottom of the fraction (the denominator) is 0. As a result, these are prohibited. Use the equal sign with a line across it to indicate these constraints, which means “x cannot equal…”
These are the non-permissible values for the expressions above:
x≠-2 x≠2 x≠ 2, 4 x≠ 1,2
Here is an example of an equation, then to be simplified to non-permissible values:
So, the non-permissible values would be 2 and 4, in other words x≠ 2,4
Let’s try a harder example:
We can factor both the top and bottom and simplify from there.
From here our non permissible values are: -3, -5. So x≠ -3, -5