Now we are 13 weeks into Pre-calc 11, and this week we dragged our focus into the new unit Rational Expressions. In this blog post, I’ll go over adding and subtracting Rational expressions with variables in the denominator.
Let’s start with our first example:
1.0
1.1
1.2
1.3
1.4
1.5
2.0
This expression looks very complicated, right? But one step that will make this problem ten times easier to solve is to completely factor the denominator and the nominator before adding/subtracting anything. Looking at step 1.1 above I have completely factored all expressions at the top and bottom in both fractions. When I factored them out it’s clear that there’s one binomial in both fractions that’s common in both top and bottom the key here is that they cancel each other out to equal 1 that’s because we are dividing them by one another now we are left with what is showing in step 1.2 here it’s a subtraction question to make it lighter to deal with let’s flip the signs of the second term (we are multiplying the – by the binomial at the top of the fraction. A close look on what’s happening -(x-2) we are just multiplying the coefficient by both terms inside the bracket). Now we move to step 1.4 we know the usual rules for adding/subtracting fractions right? we always have to get a common denominator to reach there we have to multiply both sides by the opposite denominator of each other; as I demonstrated in step 1.4 I turned both fractions into one large fraction and took the denominator of the first fraction and multiplied the 2nd fraction and the opposite back to the 1st fraction this way I’ve reached a common denominator for this expression and now we can reduce it out into the simplest form possible in step 1.5 I have foiled out the binomials and we just have to have to collect like terms to reduce the terms. And we end up with 