Step by step
The question
Question: solve 5/(x + 2) = 1 + 3/(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.
Plain numbers go together.
2 + 3 = 5.
Now we have 5 = x + 5.
Let's swap the two sides, so x is on the left.
4 Remove the + 5
We want x by itself.
The + 5 is in the way.
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.
5 − 5 = 0.
So x = 0!
5 Check
Let's check: put 0 in place of x.
First the left side.
Now the right side.
Both sides are 5/2.
So x = 0 is right!
Let's look back.
First: remove the fractions.
Then: open the brackets.
Then: group like terms.
Then: remove the + 5.
Last: check.