Step by step
The question
Question: solve (x + 1)/(x − 2) = 4.
x is in the bottom of a fraction.
We write 4 as 4/1.
Now both sides are fractions.
1 Cross multiply
When two fractions are equal, we can cross multiply.
These two are equal.
Work out the multiplications.
2 Open the brackets
The 4 in front of the bracket multiplies every part inside.
So we write 4 times each part.
A bracket with a plus or nothing in front can just be removed.
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 x from the left side.
To remove x, we take away x.
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.
x and − x make zero.
Cross them out.
4x − x = 3x.
Now we have 1 = 3x − 8.
Let's swap the two sides, so x is on the left.
We want x by itself.
Two things are stuck to x: times 3 and − 8.
The − 8 is on the outside, so it comes off first.
Then the times 3.
4 Remove the − 8
To remove − 8, we add 8.
We do it on both sides, so they stay equal.
− 8 and + 8 make zero.
Cross them out.
1 + 8 = 9.
Now we have 3x = 9.
5 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just x is left.
9 divided by 3 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 4.
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 − 8.
Then: remove the 3.
Last: check.