Simplify 5/(2x) - 1/(4x) Step by Step

Step by step

The question

Question: work out 5/2x − 1/4x.

52x − 14x

1 Find the common bottom

The bottoms are 2x and 4x.

bottoms: 2x and 4x

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

For the numbers: 4 is the smallest number both 2 and 4 go into.

It is 4x.

common bottom = 4x

Careful!

We can't take away the tops and take away the bottoms.

Fractions need the same bottom first.

Careful: not 4−2x ✗

2 Make the bottoms the same

The first fraction is missing 2.

We multiply its top and bottom by 2.

The second fraction already has it.

2/2 is 1, so the value stays the same.

= 5 × 22x × 2 − 14x

3 Take away the tops

Now one fraction: (5 × 2 − 1)/4x.

= 5 × 2 − 14x

On top: 5 × 2 − 1 is 9.

5 × 2 − 1 = 9

So the top is 9.

= 94x

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 9/4x.

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.

5/2 take away 1/4 is 9/4.

Question: 52(1) − 14(1) = 52 − 14 = 94

Now in our answer.

We get 9/4 too.

Answer: 94(1) = 94

Both are 9/4.

So 9/4x is right!

Let's look back.

First: find the common bottom.

Then: make the bottoms the same.

Then: take away the tops.

Then: cross out the same.

Last: check.

Answer