Simplify 4/(x - 1) + 1/(x - 1)

Step by step

The question

Question: add 4/(x − 1) + 1/(x − 1).

1 Add the tops

The bottoms are already the same.

We add the tops.

The bottom stays.

Careful!

The bottoms are the same.

Only the tops are added.

The bottom stays.

Now one fraction: (4 + 1)/(x − 1).

On top: 4 + 1 is 5.

So the top is 5.

2 Cross out the same

Is a whole factor on top the same as one on the bottom?

No.

So nothing crosses out.

We leave the bottom as factors.

So the answer is 5/(x − 1).

The bottoms can't be 0.

So x can't be 1.

3 Check

Let's check with a number: x = 2.

First in the question.

4 plus 1 is 5.

Now in our answer.

We get 5 too.

Both are 5.

So 5/(x − 1) is right!

Let's look back.

First: add the tops.

Then: cross out the same.

Last: check.