Step by step
The question
Question: simplify 3/x(x + 1) × (x + 1)/6.
1 Factor every part
First the bottom of the first fraction: x(x + 1).
It is already factored: x(x + 1) means x times (x + 1).
We just read the factors.
So the bottom of the first fraction is x(x + 1).
2 Cross out the same
Careful!
We cross out only a whole bracket, or a whole x, that multiplies everything.
Never one part of a bracket.
Now every part is factored.
A bracket on any top and the same bracket on any bottom make 1.
(x + 1)/(x + 1) is 1.
Cross them out.
3 and 6 can both be divided by 3.
3 becomes 1, 6 becomes 2.
3 Multiply what is left
Top times top, bottom times bottom.
What is left is 1/2x.
One more thing: the bottom of the question can't be 0.
So x can't be −1 or 0.
4 Check
Let's check with a number: x = 2.
First in the question.
We get 1/4.
Now in our answer.
We get 1/4 too.
Both are 1/4.
So 1/2x is right!
Let's look back.
First: factor every part.
Then: cross out the same.
Then: multiply what is left.
Last: check.