Step by step
The question
Question: simplify this fraction.
On top: 3 over x.
At the bottom: 6/x².
A fraction with fractions inside is called a complex fraction.
1 Find the common bottom
The small fractions have bottoms x and x².
The smallest thing they all go into is x².
2 Times x² on top and bottom
x² over x² is 1.
Times 1 does not change the value.
We multiply the top and the bottom by x².
Then the small fractions go away.
3 Multiply every part
Every part times x².
x² times 3/x: the bottom x goes into x², so we get 3x.
x² times 6/x²: the bottom x² goes into x², so we get 6.
So we get 3x/6.
No more small fractions!
4 Simplify
Every part, on the top and the bottom, can be divided by 3.
So we divide the top and the bottom by it.
So the answer is x/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 3/2, the bottom is 3/2.
Top divided by bottom: 1.
Our answer with x = 2 gives 1 too.
It works!
Let's look back.
First: find the common bottom.
Then: times x² on top and bottom.
Then: multiply every part.
Then: simplify.
Last: check.