Simplify (2x(x + 1))/(4x^2) Step by Step

Step by step

The question

Question: simplify 2x(x + 1)/4x².

A fraction with x in it is called a rational expression.

2x(x + 1)4x²

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.

69 = 2 × 33 × 3 = 23

1 Factor the top

We look at the top: 2x(x + 1).

= 2x(x + 1)

It is already factored: 2x(x + 1) means 2x times (x + 1).

We just read the factors.

2x(x + 1) = 2x × (x + 1)

So the top is 2x(x + 1).

= 2x(x + 1)

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.

Careful: only whole brackets cross out

Now we write the fraction with the factors: 2x(x + 1)/4xx.

= 2x(x + 1)4xx

x/x is 1.

Cross them out.

2 and 4 can both be divided by 2.

2 becomes 1, 4 becomes 2.

3 Write what is left

What is left is (x + 1)/2x.

= x + 12x

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

So x can't be 0.

x ≠ 0

4 Check

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

First in the question.

We get 3/4.

Question: 2(2)(2 + 1)4(2)² = 1216 = 34

Now in our answer.

We get 3/4 too.

Answer: 2 + 14 = 34

Both are 3/4.

So (x + 1)/2x is right!

Let's look back.

First: factor the top.

Then: cross out the same.

Then: write what is left.

Last: check.

Answer