Simplify x/(x + 2) × (x + 2)/(x(x

Step by step

The question

Question: simplify x/(x + 2) × (x + 2)/x(x − 1).

xx + 2 × x + 2x(x − 1)

1 Factor every part

First the bottom of the second fraction: x(x − 1).

= x(x − 1)

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

We just read the factors.

x(x − 1) = x × (x − 1)

So the bottom of the second fraction is x(x − 1).

= x(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 every part is factored.

A bracket on any top and the same bracket on any bottom make 1.

= x~~(x + 2)~~ × ~~(x + 2)~~x(x − 1)

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

Cross them out.

x/x is 1.

Cross them out.

3 Multiply what is left

Top times top, bottom times bottom.

What is left is 1/(x − 1).

= 1x − 1

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

So x can't be −2, 0 or 1.

x ≠ −2, 0, 1

4 Check

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

First in the question.

We get 1.

Question: 22 + 2 × 2 + 22(2 − 1) = 24 × 42 = 1

Now in our answer.

We get 1 too.

Answer: 12 − 1 = 1

Both are 1.

So 1/(x − 1) is right!

Let's look back.

First: factor every part.

Then: cross out the same.

Then: multiply what is left.

Last: check.

Answer