Simplify 1/(2x) + 1/(3x) Step by Step

Step by step

The question

Question: add 1/2x + 1/3x.

12x + 13x

1 Find the common bottom

The bottoms are 2x and 3x.

bottoms: 2x and 3x

The common bottom must have every factor of both bottoms, each one once.

For the numbers: 6 is the smallest number both 2 and 3 go into.

It is 6x.

common bottom = 6x

Careful!

We can't add the tops and add the bottoms.

Fractions need the same bottom first.

Careful: not 25x ✗

2 Make the bottoms the same

The first fraction is missing 3.

We multiply its top and bottom by 3.

The second fraction is missing 2.

We multiply its top and bottom by 2.

3/3 is 1, so the value stays the same.

= 1 × 32x × 3 + 1 × 23x × 2

3 Add the tops

Now one fraction: (1 × 3 + 1 × 2)/6x.

= 1 × 3 + 1 × 26x

On top: 1 × 3 + 1 × 2 is 5.

1 × 3 + 1 × 2 = 5

So the top is 5.

= 56x

4 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 5/6x.

The bottoms can't be 0.

So x can't be 0.

x ≠ 0

5 Check

Let's check with a number: x = 1.

First in the question.

1/2 plus 1/3 is 5/6.

Question: 12(1) + 13(1) = 12 + 13 = 56

Now in our answer.

We get 5/6 too.

Answer: 56(1) = 56

Both are 5/6.

So 5/6x is right!

Let's look back.

First: find the common bottom.

Then: make the bottoms the same.

Then: add the tops.

Then: cross out the same.

Last: check.

Answer