Step by step
The question
Question: simplify (x + 2)/(x − 1) × (x² − 1)/(3x + 6).
1 Factor every part
First the top of the second fraction: x² − 1.
x² − 1 is x² minus 1 squared.
A square minus a square is the plus bracket times the minus bracket.
So the top of the second fraction is (x + 1)(x − 1).
Now the bottom of the second fraction: 3x + 6.
3 and 6 can both be divided by 3.
We take 3 out.
What is left goes in the bracket.
So the bottom of the second fraction is 3(x + 2).
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 + 2)/(x + 2) is 1.
Cross them out.
(x − 1)/(x − 1) is 1.
Cross them out.
3 Multiply what is left
Top times top, bottom times bottom.
What is left is (x + 1)/3.
One more thing: the bottom of the question can't be 0.
So x can't be −2 or 1.
4 Check
Let's check with a number: x = 2.
First in the question.
We get 1.
Now in our answer.
We get 1 too.
Both are 1.
So (x + 1)/3 is right!
Let's look back.
First: factor every part.
Then: cross out the same.
Then: multiply what is left.
Last: check.