This week in math I had a question on rational expressions that seemed very tricky at first. The question was:

then i start with the first step

1.factoring:

The second step finding the Common denominator of them

and than write them with the common denominator all together

after all these steps now we can do the adding or anything that the question asks:

now we can see, we could still factor the numerator to 4

And the final answer will be

When working with rational expressions, we always need to check which numbers make the denominator zero.
Because division by zero is impossible → so those numbers are not allowed.

In this question:

1. First denominator:

If:

or

, the denominator becomes zero.

So these two values ​​are not allowed.

2. Second denominator:

If:

or

, the denominator becomes zero.

(We already had x = -8)

3. Final result (Domain Restrictions)

Numbers that we cannot substitute for x:

Because each of these values ​​causes the denominator to become zero.

As soon as the denominator becomes zero, the whole expression becomes meaningless.