Step by step
The question
Question: solve 2/(x + 3) = 4/(x + 9).
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 left 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 18 = 2x + 12.
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 + 12.
The + 12 is on the outside, so it comes off first.
Then the times 2.
4 Remove the + 12
To remove + 12, we take away 12.
We do it on both sides, so they stay equal.
+ 12 and − 12 make zero.
Cross them out.
18 − 12 = 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 1/3.
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 + 12.
Then: remove the 2.
Last: check.