Step by step
The question
Question: solve 4/(x − 2) + 1 = 3.
First: a bottom can never be 0.
x = 2 makes x − 2 0.
So x ≠ 2.
1 Remove the fractions
The bottom is (x − 2).
Times (x − 2) will remove it.
We multiply every part by (x − 2).
We do it on both sides, so they stay equal.
(x − 2) divided by (x − 2) is 1.
(x − 2) times 1 is (x − 2).
(x − 2) times 3 is 3(x − 2).
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.
A bracket with a plus or nothing in front can just be removed.
Work out each multiplication.
3 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
Plain numbers go together.
4 − 2 = 2.
Now we have 2 + x = 3x − 6.
4 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 2 = 2x − 6.
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 − 6.
The − 6 is on the outside, so it comes off first.
Then the times 2.
5 Remove the − 6
To remove − 6, we add 6.
We do it on both sides, so they stay equal.
− 6 and + 6 make zero.
Cross them out.
2 + 6 = 8.
Now we have 2x = 8.
6 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.
8 divided by 2 is 4.
So x = 4!
7 Check
Let's check: put 4 in place of x.
First the left side.
Now the right side.
Both sides are 3.
So x = 4 is right!
Let's look back.
First: remove the fractions.
Then: open the brackets.
Then: group like terms.
Then: get x on one side.
Then: remove the − 6.
Then: remove the 2.
Last: check.