This week in Pre-Calc 11 we learned how to add and subtract rational expressions. I chose this topic because adding and subtracting rational expressions is the foundation of our current unit. Let’s try a question now!

When approaching a rational expression question the first thing you should always do is to see whether the question is factorable or if there is a difference of squares. However in our question here we can do neither so we put brackets around to indicate that we already have checked if it’s factorable.

Next step we just like adding regular fractions, we need to find the LCD o (Lowest Common Denominator) in order to add these fractions this being 3(x-2). Now we multiply the bottom and top then put it into a high school fraction (that one big long fraction).

That now leaves us with this and now we check if we can simplify this expression.

And oh it doesn’t look like a multiple of 10 can get a sum of 5 leaving us with this equation.

Lastly we now need to set a restriction for X. We do this by looking at the denominator in our example here it’s -2 so what cancels out negative 2? Positive 2 right? Meaning x cannot be +2.

Now let’s try a subtraction question.

Just Like an additional question, our first step is always to see whether the expression is factorable or has a difference in squares. In this case we don’t see any here and the denominator has the same variable.

Another rule we have to add before turning it into a high school fraction is that when dealing with binomials, especially subtracting, we should flip the signs. I know that may seem confusing but stay with me now. The reason we do this is because when we turn binomials into high school fractions (the one big fraction we often forget about what the + or – signs apply to what.

Now we put like terms together leaving us with then we set our restriction leaving us being 0 be cause 0 x 0 is 0 cancels itself out.

AND TADA!!! Now you learnt how to do subtract and add rational expressions