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

Step by step

The question

Question: simplify this fraction.

On top: x + 1 over x.

At the bottom: 2 over x.

A fraction with fractions inside is called a complex fraction.

x + 1x2x

1 Find the common bottom

The small fraction has the bottom x.

The smallest thing they all go into is x.

small bottoms: x

common bottom: x

Careful!

We multiply EVERY part by x, also the part with no small bottom.

Leaving it out is the usual mistake.

Careful: every part times x, the whole numbers too

2 Times x on top and bottom

x/x is 1.

Times 1 does not change the value.

xx = 1

We multiply the top and the bottom by x.

Then the small fractions go away.

= x × (x + 1x)x × (2x)

3 Multiply every part

Every part times x.

x times x is x².

x times 1/x: the bottom x goes into x, so we get 1.

x × x = x²

x × 1x = 1

x × 2x = 2

So we get (x² + 1)/2.

No more small fractions!

= x² + 12

4 Simplify

Is there a number or an x that goes into every part, top and bottom?

No.

So it is already simple.

So the answer is (x² + 1)/2.

nothing goes into every part

One more thing: no bottom can be 0.

So x can't be 0.

x ≠ 0

5 Check

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

In the question, the long way: the top is 5/2, the bottom is 1.

x = 2: top 2 + 12 = 52, bottom 1 = 1

Top divided by bottom: 5/2.

question: 52 ÷ 1 = 52

Our answer with x = 2 gives 5/2 too.

It works!

answer: 2² + 12 = 52

Let's look back.

First: find the common bottom.

Then: times x on top and bottom.

Then: multiply every part.

Then: simplify.

Last: check.

Answer