First, let's simplify the expressions within the brackets:

а + 4√2а + 8 = а(1 + 4√2) + 8
√а - √8 = √а - 2√2

Now we can substitute these expressions in the numerator:

(а(1 + 4√2) + 8) * (√a - 2√2)

Next, let's expand the numerator:

а√а + 4а√2 + 8√а + 32 - 2а√2 - 8√2

Combining like terms, we get:

а√а + 8√а + 8√2 + 32 - 2а√2 - 8√2

Now, let's simplify the denominator, which is:

а√а + 8√а - 2а√2 - 16√2

Dividing the numerator by the denominator, we get:

(а√а + 8√а + 8√2 + 32 - 2a√2 - 8√2) / (а√а + 8√а - 2a√2 - 16√2)