In the first video, we are going to add and subtract rational expressions.
Simply combine the numerator and the denominator together if the denominators are the same and we have
Let’s look at another example:
Since the denominators are not the same, multiple each fraction to achieve the least common multiple
Now, we can add the terms together
In order to reduce the expression, factor if necessary
Reduce, and our final answer is
Let’s go over how to add and subtract rational expressions.
We have two rational expressions here
Just like any fractions that need to add or subtract, we have to have a common denominator.
In this case, we do.
So, we have the same denominator and then just add the numerator.
Our answer is
Let’s look at a more difficult one.
Again, we have common denominators. So we’ll just copy it.
We’ll subtract the numerator as necessary.
Then distribute the negative sign
Then, let’s combine the like terms
Let’s look at an example where we don’t have common denominators.
What we want to do first is to write this with common denominators.
So, we need the least common multiple of the two denominators.
What can we multiply these by to give us something that will equal each other?
Let’s look at the numbers first and identify the least common multiple.
will be ,
We multiplied by and by .
So here’s our solution:
Now we can add these together.
Let’s look at it further.
We can still reduce this since there’s a factor
In the second video, we are going to add and subtract rational expressions that are more complex.
Multiply each fraction to achieve the least common multiple
Use the distributive property to multiply
Now that we have common denominators, add the numerators together
Factor any expression if necessary
Since nothing can be reduced, we are going back to the original expression
Use FOIL (First, Outside, Inside, Last) to multiply
Combine like terms, and we have
Let’s go over how to add and subtract rational expressions part 2.
We’re going to focus on binomials on the denominator.
First, we want to write this with common denominators.
What could be the least common multiple of these two?
Let’s take a step back and take a look at adding fractions.
If we have
what is the least common multiple of and ?
We got that by simply multiplying the two numbers.
Now, we’ll have
So, we’ll do the same thing here.
Let’s just multiply these together.
Now, let’s add the numerators together.
The reason why we didn’t multiply the denominators together is because it’s a lot easier to factor this way.
Now, we can factor the numerator only and keep the denominator as it is.
But there isn’t anything to cancel out.
So, let’s just solve it.
And our answer is
This format is also acceptable:
Let’s look at this one
So, we’ll just multiply the denominators together to get the common denominator.
This will be a bit more complicated because we’re going to multiply a binomial to a trinomial.
Multiplying these is going to give us a big expression. If we just multiply them upfront.
This is going to be confusing.
We’ll still get the correct answer but this is a lot of work.
So, let’s look at another option.
What we can do is to look at the factors of these denominators.
stays as is
Let’s factor out
The first denominator is already , so we’ll just multiply it by
At this point, we already have common denominators.
The numerator for the second expression stays the same because all we did was just to factor its denominator.
The denominator didn’t change in the second expression.
We have like terms here so let’s combine.
Our answer is
This can’t be factored and reduced further. So, it’s the final answer.