Question

find the product of (x^2-3x=5) with the quotient of (10x^6-15x^5-5x^3)/5x^3. I don't understand!!

Answer 1

It's jut a matter of multiplying fractions. It would be easy to do

3 * 7/8, right? Just do 3*7/8

This is the same thing, but is just a little messier:

I assume a typo on the "=" sign. It is useless.
(x^2-3x-5) * (10x^6-15x^5-5x^3)/5x^3)

Looks pretty bad, so let's factor stuff and see what drops out:

x^2 - 3x - 5 doesn't factor easily, so let's skip it for now.

10x^6-15x^5-5x^3 = 5x^3 (2x^3 - 3x^2 - 1) = 5x^3 * (x-1)^2 (2x+1)

So, the fraction loses its denominator and is just

(x-1)^2 (2x+1)

So, we end up with

(x^2 - 3x - 5) * (x-1)^2 * (2x+1)

Can't see much more simplification here.