Step by step
The question
Question: simplify this fraction.
On top: 1 − 1 over x.
At the bottom: 3 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.
Careful!
We multiply EVERY part by x, also the part with no small bottom.
Leaving it out is the usual mistake.
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 1 is x.
x times 1/x: the bottom x goes into x, so we get 1.
So we get (x − 1)/3.
No more small fractions!
4 Simplify
Is there a number or an x that goes into every part, top and bottom?
No.
So it is already simple.
So the answer is (x − 1)/3.
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 1/2, the bottom is 3/2.
Top divided by bottom: 1/3.
Our answer with x = 2 gives 1/3 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.