Step by step
The question
Question: solve 2x/(x − 1) − 2/(x − 1) = 3.
First: a bottom can never be 0.
x = 1 makes x − 1 0.
So x ≠ 1.
1 Remove the fractions
The bottom is (x − 1).
Times (x − 1) will remove it.
We multiply every part by (x − 1).
We do it on both sides, so they stay equal.
(x − 1) divided by (x − 1) is 1.
(x − 1) divided by (x − 1) is 1.
(x − 1) times 3 is 3(x − 1).
Write what is left.
No more fractions!
2 Open the brackets
The 3 in front of the bracket multiplies every part inside.
So we write 3 times each part.
Work out each multiplication.
3 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the 2x from the left side.
To remove 2x, we take away 2x.
We do it on both sides, so they stay equal.
2x and − 2x make zero.
Cross them out.
3x − 2x = x.
Now we have −2 = x − 3.
Let's swap the two sides, so x is on the left.
4 Remove the − 3
We want x by itself.
The − 3 is in the way.
To remove − 3, we add 3.
We do it on both sides, so they stay equal.
− 3 and + 3 make zero.
Cross them out.
−2 + 3 = 1.
So x = 1!
But x = 1 is the x that is not allowed: it makes a bottom 0.
So there is no solution.
Let's look back.
First: remove the fractions.
Then: open the brackets.
Then: get x on one side.
Last: remove the − 3.