Simplify (3 - x)/(x - 3)

Step by step

The question

Question: simplify (3 − x)/(x − 3).

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: 3 − x.

The x part has a minus.

We take the minus out, in front of a bracket.

Every sign inside changes.

So the top is −(x − 3).

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 − 3)/(x − 3).

(x − 3)/(x − 3) is 1.

Cross them out.

3 Write what is left

What is left is −1.

One more thing: the bottom of the question can't be 0.

So x can't be 3.

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 −1 is right!

Let's look back.

First: factor the top.

Then: cross out the same.

Then: write what is left.

Last: check.