Step by step
The question
Question: solve 2/x + 3 = 1/x + 4.
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.
x times 4 is 4x.
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 3x from the left side.
To remove 3x, we take away 3x.
We do it on both sides, so they stay equal.
+ 3x and − 3x make zero.
Cross them out.
4x − 3x = x.
Now we have 2 = 1 + x.
Let's swap the two sides, so x is on the left.
3 Remove the 1
We want x by itself.
The 1 is in the way.
To remove 1, we take away 1.
We do it on both sides, so they stay equal.
1 and − 1 make zero.
Cross them out.
2 − 1 = 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 5.
So x = 1 is right!
Let's look back.
First: remove the fractions.
Then: get x on one side.
Then: remove the 1.
Last: check.