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

Step by step

The question

Question: simplify 2x/(x² + 3x).

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

2xx² + 3x

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: x² + 3x.

= x² + 3x

Every part has x.

We take x out.

What is left goes in the bracket.

x² ÷ x = x, 3x ÷ x = 3

So the bottom is x(x + 3).

= x(x + 3)

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 + 3).

= 2xx(x + 3)

x/x is 1.

Cross them out.

3 Write what is left

What is left is 2/(x + 3).

= 2x + 3

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

So x can't be −3 or 0.

x ≠ −3, 0

4 Check

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

First in the question.

We get 2/5.

Question: 2(2)2² + 3(2) = 410 = 25

Now in our answer.

We get 2/5 too.

Answer: 22 + 3 = 25

Both are 2/5.

So 2/(x + 3) is right!

Let's look back.

First: factor the bottom.

Then: cross out the same.

Then: write what is left.

Last: check.

Answer