To simplify the expression, let's break it down step by step:

First, let's simplify the numerator: 3^8 - 3^9

Since both terms have the same base (3), we can subtract the exponents: 8 - 9 = -1

So, the numerator simplifies to 3^-1.

Next, let's simplify the denominator: 3^8 + 3^8

Since both terms have the same base (3), we can add the exponents: 8 + 8 = 16

So, the denominator simplifies to 3^16.

Finally, let's simplify the last term: 3^8 x 5

Since both terms have the same base (3), we can multiply the exponents: 8 + 1 = 9

So, the last term simplifies to 3^9.

Now, let's put it all together:

3^-1 / 3^16 + 3^9

To combine the terms with the same base, we subtract the exponents in the denominator: 3^-1 / 3^(16-9) + 3^9

Simplifying further, we have: 3^-1 / 3^7 + 3^9

To combine the terms with the same base, we add the exponents in the denominator: 3^-1 / 3^7 + 3^9

Now, let's simplify the expression:

3^-1 is the same as 1/3^1, so we have: 1/3 / 3^7 + 3^9

To simplify further, we can rewrite 1/3 as 3^-1: 3^-1 / 3^7 + 3^9

Now, we can combine the terms with the same base: 3^(-1-7) + 3^9

Simplifying the exponents, we have: 3^-8 + 3^9

Therefore, the simplified expression is: 1/3^8 + 3^9