Step by step
The question
Question: solve 5/x − 1/2 = 2 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 bottoms are x and 2.
2x can be divided by all of them.
We multiply every part by 2x.
We do it on both sides, so they stay equal.
2x divided by x is 2.
2x divided by 2 is x.
2x divided by x is 2.
Write what is left.
No more fractions!
2 Remove the 10
We want x by itself.
The 10 is in the way.
To remove 10, we take away 10.
We do it on both sides, so they stay equal.
10 and − 10 make zero.
Cross them out.
4 − 10 = −6.
Now we have −x = −6.
3 Remove the −1
−x means −1 times x.
We want just x.
To remove times −1, we divide by −1.
We do it on both sides, so they stay equal.
−1 divided by −1 is 1.
So just x is left.
−6 divided by −1 is 6.
So x = 6!
4 Check
Let's check: put 6 in place of x.
First the left side.
Now the right side.
Both sides are 1/3.
So x = 6 is right!
Let's look back.
First: remove the fractions.
Then: remove the 10.
Then: remove the −1.
Last: check.