To simplify the given expression, let's analyze and simplify each fraction one at a time.
The first fraction is (3x+15)/(x+8). We can see that there's a common factor of 3 in the numerator. If we factor out the 3, we get:
(3x+15) = 3*(x+5)
Now our first fraction looks like this: 3*(x+5)/(x+8). We can't simplify this fraction any further since there's no common factor in the numerator and denominator.
The second fraction is (5x+40)/(9x+45). Here, there's a common factor of 5 in the numerator. When we factor that out, we get:
(5x+40) = 5*(x+8)
Now our second fraction looks like this: 5*(x+8)/(9x+45)
Looking at the denominator of this fraction, we can factor out 9:
(9x+45) = 9*(x+5)
Which makes our second fraction look like: 5*(x+8)/9*(x+5). Here, it's clear that the denominator and numerator don't have any factor in common.
Now, let's multiply the first and second fractions:
[3*(x+5)/(x+8)] * [5*(x+8)/9*(x+5)]
In this expression, we can simplify by cancelling out the common terms from the numerator and the denominator, (x+5) and (x+8). What we are left with is 3/9 multiplied by 5/1, which simplifies to 5/3 after reducing the fraction to the simplest form.
Hence, the simplified form of the given expression is 5/3.