Step by step
The question
Question: simplify (x − 1)/(x − 1)(x + 4).
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 bottom
We look at the bottom: (x − 1)(x + 4).
It is already factored: (x − 1)(x + 4) means (x − 1) times (x + 4).
We just read the factors.
So the bottom is (x − 1)(x + 4).
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 + 4).
(x − 1)/(x − 1) is 1.
Cross them out.
3 Write what is left
What is left is 1/(x + 4).
One more thing: the bottom of the question can't be 0.
So x can't be −4 or 1.
4 Check
Let's check with a number: x = 2.
First in the question.
We get 1/6.
Now in our answer.
We get 1/6 too.
Both are 1/6.
So 1/(x + 4) is right!
Let's look back.
First: factor the bottom.
Then: cross out the same.
Then: write what is left.
Last: check.