Step by step
The question
Question: simplify (x² − 1)/(x − 1).
A fraction with x in it is called a rational expression.
We make it simpler like a number fraction.
6/9: both have a 3 in them.
3/3 is 1, so 2/3 is left.
We do the same with brackets.
1 Factor the top
We look at the top: 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 is (x + 1)(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 we write the fraction with the factors: (x + 1)(x − 1)/(x − 1).
(x − 1)/(x − 1) is 1.
Cross them out.
3 Write what is left
What is left is x + 1.
One more thing: the bottom of the question can't be 0.
So x can't be 1.
4 Check
Let's check with a number: x = 2.
First in the question.
We get 3.
Now in our answer.
We get 3 too.
Both are 3.
So x + 1 is right!
Let's look back.
First: factor the top.
Then: cross out the same.
Then: write what is left.
Last: check.