Step by step
The question
Question: simplify this fraction.
On top: 3/x².
At the bottom: 9 over x.
A fraction with fractions inside is called a complex fraction.
1 Find the common bottom
The small fractions have bottoms x² and x.
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/x²: the bottom x² goes into x², so we get 3.
x² times 9/x: the bottom x goes into x², so we get 9x.
So we get 3/9x.
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 1/3x.
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 3/4, the bottom is 9/2.
Top divided by bottom: 1/6.
Our answer with x = 2 gives 1/6 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.