Step by step
The question
Question: solve 6/x − 1 = 2.
First: a bottom can never be 0.
x at the bottom can't be 0.
So x ≠ 0.
1 Remove the fractions
The bottom is x.
Times x will remove it.
We multiply every part by x.
We do it on both sides, so they stay equal.
x divided by x is 1.
x times 1 is x.
x times 2 is 2x.
Write what is left.
No more fractions!
2 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 add x.
We do it on both sides, so they stay equal.
− x and + x make zero.
Cross them out.
2x + x = 3x.
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 2.
So x = 2 is right!
Let's look back.
First: remove the fractions.
Then: get x on one side.
Then: remove the 3.
Last: check.