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

Step by step

The question

Question: simplify (x² + 3x)/x(x − 2).

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

x² + 3xx(x − 2)

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: 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 top is x(x + 3).

= x(x + 3)

2 Factor the bottom

We look at the bottom: x(x − 2).

= x(x − 2)

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

We just read the factors.

x(x − 2) = x × (x − 2)

So the bottom is x(x − 2).

= x(x − 2)

3 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: x(x + 3)/x(x − 2).

= x(x + 3)x(x − 2)

x/x is 1.

Cross them out.

4 Write what is left

What is left is (x + 3)/(x − 2).

= x + 3x − 2

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

So x can't be 0 or 2.

x ≠ 0, 2

5 Check

Let's check with a number: x = 1.

First in the question.

We get −4.

Question: 1² + 3(1)1(1 − 2) = 4−1 = −4

Now in our answer.

We get −4 too.

Answer: 1 + 31 − 2 = −4

Both are −4.

So (x + 3)/(x − 2) is right!

Let's look back.

First: factor the top.

Then: factor the bottom.

Then: cross out the same.

Then: write what is left.

Last: check.

Answer