Step by step
The question
Question: solve x/(x + 2) + 1 = 6/(x + 2).
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) divided by (x + 2) 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 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the x terms go together.
x + x = 2x.
Now we have 2x + 2 = 6.
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.
6 − 2 = 4.
Now we have 2x = 4.
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.
4 divided by 2 is 2.
So x = 2!
6 Check
Let's check: put 2 in place of x.
First the left side.
Now the right side.
Both sides are 3/2.
So x = 2 is right!
Let's look back.
First: remove the fractions.
Then: open the brackets.
Then: group like terms.
Then: remove the + 2.
Then: remove the 2.
Last: check.