Step by step
The question
Question: simplify (3x − 6)/(x − 2).
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: 3x − 6.
3 and 6 can both be divided by 3.
We take 3 out.
What is left goes in the bracket.
So the top 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 we write the fraction with the factors: 3(x − 2)/(x − 2).
(x − 2)/(x − 2) is 1.
Cross them out.
3 Write what is left
What is left is 3.
One more thing: the bottom of the question can't be 0.
So x can't be 2.
4 Check
Let's check with a number: x = 1.
First in the question.
We get 3.
Now in our answer.
We get 3 too.
Both are 3.
So 3 is right!
Let's look back.
First: factor the top.
Then: cross out the same.
Then: write what is left.
Last: check.