Practice: Algebra (fractions)

It is strange that this question has "x" in it, but as the "x" is in each term we can effectively ignore it and treat this as a fraction question. So as always we need common denominators, we could do everything at once, but let's do it in small steps, starting with the first two terms. We will cross multiply, and combine the terms:

now we can work on the last two terms, again cross multiplying and combining the terms. At the end, we can leave it as a top-heavy fraction as the question doesn't specify, or we can turn this into a mixed number:

First lets convert these mixed numbers into top-heavy fractions:

now let's make common denominators by cross multiplying, and then we can add the result:

now we can multiply tops and bottoms. Then as they are both factors of five, we can simplify by five, your calculator will do this for you! I just wanted to make every step explicit!

Let's write out the question and then turn that division into a multiplication using KFC (Keep Flip Change).

Next, we can cancel out like terms, and we are left with our answer:

Ok so let's start with the bracket. We are going to turn those mixed numbers to top heavy fractions:

lets use KFC (Keep Flip Change) to turn this into a multiplication

Now we can simplify this before we continue

We can finally work on the right hand side, and convert the mixed number into a top heavy fraction

At the end, we just need common denominators, and we are done! This is fine, but it could also be written as a mixed number 6 and 1/6

Adding fractions is harder than multiplication!

So first things first, let's see what we can cancel

now we need a common denominator to add these two fractions together.

Once we have a common denominator, we can just add them together. This is about as good as we can get, the question doesn't specify how to write the answer, so this will do. With simplification questions, it's hard to know when to stop. I think this is good enough.

Let's transpose this to make "a" the subject, first we can subtract "ut" from both sides:

Then we can remove the 1/2 if we multiply both sides by 2

Let's divide both sides by t^2

and we are done!

Ok, first of all we can turn that divide into a multiplication using KFC (Keep Flip Change)

Then we can cancel a lot of the terms.

We can combine the two square roots to make a whole

And we have our final answer.