Make x the subject of k = (x - 1)/(x + 2)

Step by step

The question

Question: make x the subject of k = (x − 1)/(x + 2).

The subject is the letter on its own: we want x = ...

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Here x is in two places, so we must bring them together.

1 Clear the fraction

The bottom, (x + 2), is in the way.

Times (x + 2) removes it.

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

(x + 2) divided by (x + 2) is 1.

Only the top is left.

Now we have k(x + 2) = x − 1.

2 Open the brackets

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

k times every part of (x + 2).

3 Get the x terms on one side

x is on the right.

To remove it, we take away x.

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

Careful!

A term that moves to the other side changes its sign.

x becomes −x.

x and −x make zero.

Cross them out.

Now we have kx + 2k − x = −1.

2k has no x.

To remove it from the left, we take away 2k.

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

2k and −2k make zero.

Cross them out.

Now both x terms are on the left: kx − x = −1 − 2k.

4 Take x out

x is in every part.

So we take it out once, and write what is left in a bracket.

So x times (k − 1) is −1 − 2k.

5 Remove the (k − 1)

(k − 1)x means (k − 1) times x.

We want just x.

To remove times (k − 1), we divide by (k − 1).

We do it on both sides.

(k − 1) divided by (k − 1) is 1.

So just x is left.

So x = (−1 − 2k)/(k − 1).

6 Check

Let's check with numbers.

We pick k = 2.

Our answer gives x = −5.

Now we put all the numbers into the start.

First the left side.

Now the right side.

Both sides are −5.

So our answer is right!

Let's look back.

First: clear the fraction.

Then: open the brackets.

Then: get the x terms on one side.

Then: take x out.

Then: remove the (k − 1).

Last: check.