Step by step
The question
Question: simplify this fraction.
On top: 2 over x.
At the bottom: 4 over x.
A fraction with fractions inside is called a complex fraction.
1 Find the common bottom
The small fraction has the bottom x.
The smallest thing they all go into is x.
2 Times x on top and bottom
x/x is 1.
Times 1 does not change the value.
We multiply the top and the bottom by x.
Then the small fractions go away.
3 Multiply every part
Every part times x.
x times 2/x: the bottom x goes into x, so we get 2.
x times 4/x: the bottom x goes into x, so we get 4.
So we get 2/4.
No more small fractions!
4 Simplify
Every part, on the top and the bottom, can be divided by 2.
So we divide the top and the bottom by it.
So the answer is 1/2.
One more thing: no bottom can be 0.
So x can't be 0.
5 Check
Let's check with a number: x = 2.
In the question, the long way: the top is 1, the bottom is 2.
Top divided by bottom: 1/2.
Our answer with x = 2 gives 1/2 too.
It works!
Let's look back.
First: find the common bottom.
Then: times x on top and bottom.
Then: multiply every part.
Then: simplify.
Last: check.