This week in Precalc 11, I learned more about fractions with variables.
We learned that we can have unfactored expressions on the numerator and denominator.
Here is an example.
As we can see, both top and bottom can be factored so let’s do so.
From here since we have 2 of the same factors, we can just cancel them out since it is equivalent to 1 over 1. Now there is an important rule. We can only do this because the factors have a multiplication side between them. If it had a + or -, we CANNOT cancel them out. At this point we can figure out the restrictions, we need to know that the denominator cannot equal 0 so our restrictions would be +1 and -3
So here is what we end up with and this is our final answer as it cannot be factored out anymore.
Back to what to what the rule was. If I had a fraction like this, I CANNOT cancel any factors. This would be the final answer.
We also learned about adding fractions with different variable denominators.
We first make sure we can’t factor. Once we made sure, we can just multiply each side by the other denominator. The left side would be multiplied by 3y and the right side would be multiplied by 5x. We will end up with this. We can easily tell that our x restrictions would be cannot equal 0 and that our y restriction would be cannot equal 0 as well.
