Solve 4/(x - 1) = 2/(x + 1)

Step by step

The question

Question: solve 4/(x − 1) = 2/(x + 1).

Two fractions are equal.

1 Cross multiply

When two fractions are equal, we can cross multiply.

These two are equal.

Work out the multiplications.

2 Open the brackets

What is in front of a bracket multiplies every part inside.

So we write each part times what is in front.

Work out each multiplication.

3 Get x on one side

There is x on both sides.

We want x on one side only.

So we remove the 2x from the right side.

To remove 2x, we take away 2x.

We do it on both sides.

Why both sides?

The = sign means both sides are the same amount.

If we change only one side, they are not the same any more.

2x and − 2x make zero.

Cross them out.

4x − 2x = 2x.

Now we have 2x + 4 = −2.

We want x by itself.

Two things are stuck to x: times 2 and + 4.

The + 4 is on the outside, so it comes off first.

Then the times 2.

4 Remove the + 4

To remove + 4, we take away 4.

We do it on both sides, so they stay equal.

+ 4 and − 4 make zero.

Cross them out.

−2 − 4 = −6.

Now we have 2x = −6.

5 Remove the 2

2x means 2 times x.

We want just x.

To remove times 2, we divide by 2.

We do it on both sides, so they stay equal.

2 divided by 2 is 1.

So just x is left.

−6 divided by 2 is −3.

So x = −3!

6 Check

Let's check: put −3 in place of x.

First the left side.

Now the right side.

Both sides are −1.

So x = −3 is right!

Let's look back.

First: cross multiply.

Then: open the brackets.

Then: get x on one side.

Then: remove the + 4.

Then: remove the 2.

Last: check.