Step by step
The question
Question: work out 5/(x + 3) − 2/(x + 3).
5x + 3 − 2x + 3
1 Take away the tops
The bottoms are already the same.
We take away the tops.
The bottom stays.
ac − bc = a − bc
Careful!
The bottoms are the same.
Only the tops are added.
The bottom stays.
Careful: not 3x + 3 + x + 3 ✗
Now one fraction: (5 − 2)/(x + 3).
= 5 − 2(x + 3)
On top: 5 − 2 is 3.
5 − 2 = 3
So the top is 3.
= 3(x + 3)
2 Cross out the same
Is a whole factor on top the same as one on the bottom?
No.
So nothing crosses out.
We leave the bottom as factors.
So the answer is 3/(x + 3).
The bottoms can't be 0.
So x can't be −3.
x ≠ −3
3 Check
Let's check with a number: x = 1.
First in the question.
5/4 take away 2/4 is 3/4.
Question: 51 + 3 − 21 + 3 = 54 − 24 = 34
Now in our answer.
We get 3/4 too.
Answer: 3(1 + 3) = 34
Both are 3/4.
So 3/(x + 3) is right!
Let's look back.
First: take away the tops.
Then: cross out the same.
Last: check.
Answer
= 3(x + 3)