Simplify (2x)/(x(x + 5)) Step by Step | x and a bracket at the bottom

Step by step

The question

Question: simplify 2x/x(x + 5).

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

2xx(x + 5)

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 bottom

We look at the bottom: x(x + 5).

= x(x + 5)

It is already factored: x(x + 5) means x times (x + 5).

We just read the factors.

x(x + 5) = x × (x + 5)

So the bottom is x(x + 5).

= x(x + 5)

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(x + 5).

= 2xx(x + 5)

x/x is 1.

Cross them out.

3 Write what is left

What is left is 2/(x + 5).

= 2x + 5

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

So x can't be −5 or 0.

x ≠ −5, 0

4 Check

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

First in the question.

We get 2/7.

Question: 2(2)2(2 + 5) = 414 = 27

Now in our answer.

We get 2/7 too.

Answer: 22 + 5 = 27

Both are 2/7.

So 2/(x + 5) is right!

Let's look back.

First: factor the bottom.

Then: cross out the same.

Then: write what is left.

Last: check.

Answer