Step by step
The question
Question: solve 1/x + 1/2x = 3/4.
First: a bottom can never be 0.
x at the bottom can't be 0.
So x ≠ 0.
1 Remove the fractions
The bottoms are x, 2x and 4.
4x can be divided by all of them.
We multiply every part by 4x.
We do it on both sides, so they stay equal.
4x divided by x is 4.
4x divided by 2x is 2.
4x divided by 4 is x.
Write what is left.
No more fractions!
2 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
Plain numbers go together.
4 + 2 = 6.
Now we have 6 = 3x.
Let's swap the two sides, so x is on the left.
3 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.
6 divided by 3 is 2.
So x = 2!
4 Check
Let's check: put 2 in place of x.
First the left side.
Now the right side.
Both sides are 3/4.
So x = 2 is right!
Let's look back.
First: remove the fractions.
Then: group like terms.
Then: remove the 3.
Last: check.