Step by step
The question
Question: solve 3/x + 2 = 1 over x.
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 2 is 2x.
x divided by x is 1.
Write what is left.
No more fractions!
We want x by itself.
Two things are stuck to x: times 2 and + 3.
The + 3 is on the outside, so it comes off first.
Then the times 2.
2 Remove the 3
To remove 3, we take away 3.
We do it on both sides, so they stay equal.
3 and − 3 make zero.
Cross them out.
1 − 3 = −2.
Now we have 2x = −2.
3 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.
−2 divided by 2 is −1.
So x = −1!
4 Check
Let's check: put −1 in place of x.
First the left side.
Now the right side.
Both sides are −1.
So x = −1 is right!
Let's look back.
First: remove the fractions.
Then: remove the 3.
Then: remove the 2.
Last: check.