Step by step
The question
Question: solve 6/(x + 1) = 2 + 3/(x + 1).
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) times 2 is 2(x + 1).
(x + 1) divided by (x + 1) is 1.
Write what is left.
No more fractions!
2 Open the brackets
The 2 in front of the bracket multiplies every part inside.
So we write 2 times each part.
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.
2 + 3 = 5.
Now we have 6 = 2x + 5.
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 + 5.
The + 5 is on the outside, so it comes off first.
Then the times 2.
4 Remove the + 5
To remove + 5, we take away 5.
We do it on both sides, so they stay equal.
+ 5 and − 5 make zero.
Cross them out.
6 − 5 = 1.
Now we have 2x = 1.
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.
So x = 1/2!
6 Check
Let's check: put 1/2 in place of x.
First the left side.
Now the right side.
Both sides are 4.
So x = 1/2 is right!
Let's look back.
First: remove the fractions.
Then: open the brackets.
Then: group like terms.
Then: remove the + 5.
Then: remove the 2.
Last: check.