What is the product in simplest form? state any restrictions on the variable. z^2/z+1 times z^2+3z+2/z^2+3z

Hence, the product is:

such that: z≠ -1,0 and -3.

We are asked to represent the product in the simplest form along with the restrictions applied to z.

We have to evaluate the expression:

Hence,

z≠ -1,0 and -3.

Since, otherwise the denominator will be equal to zero and hence the product will not be defined.

Now, we know that:

Hence,

( since z and (z+1) term is cancelled as it was same in numerator and denominator)

Hence, the product is:

such that: z≠ -1,0 and -3.

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)