Step by step
The question
Question: solve (x + 4)/x = 3 + 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 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 3 is 3x.
x divided by x is 1.
Write what is left.
No more fractions!
2 Open the brackets
A bracket with a plus or nothing in front can just be removed.
3 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 take away x.
We do it on both sides, so they stay equal.
x and − x make zero.
Cross them out.
3x − x = 2x.
Now we have 4 = 2x + 2.
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 + 2.
The + 2 is on the outside, so it comes off first.
Then the times 2.
4 Remove the + 2
To remove + 2, we take away 2.
We do it on both sides, so they stay equal.
+ 2 and − 2 make zero.
Cross them out.
4 − 2 = 2.
Now we have 2x = 2.
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.
2 divided by 2 is 1.
So x = 1!
6 Check
Let's check: put 1 in place of x.
First the left side.
Now the right side.
Both sides are 5.
So x = 1 is right!
Let's look back.
First: remove the fractions.
Then: open the brackets.
Then: get x on one side.
Then: remove the + 2.
Then: remove the 2.
Last: check.