Step by step
The question
Question: solve 6/(x + 1) = 2/3.
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
The 2 in front of the bracket multiplies every part inside.
So we write 2 times each part.
Work out each multiplication.
Let's swap the two sides, so x is on the left.
We want x by itself.
Two things are stuck to x: times 2 and + 2.
The + 2 is on the outside, so it comes off first.
Then the times 2.
3 Remove the + 2
To remove + 2, we take away 2.
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.
+ 2 and − 2 make zero.
Cross them out.
18 − 2 = 16.
Now we have 2x = 16.
4 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.
16 divided by 2 is 8.
So x = 8!
5 Check
Let's check: put 8 in place of x.
First the left side.
Now the right side.
Both sides are 2/3.
So x = 8 is right!
Let's look back.
First: cross multiply.
Then: open the brackets.
Then: remove the + 2.
Then: remove the 2.
Last: check.