2z^3-6z^2/z^2-3z?

(2z³ - 6z²) / (z² - 3z)

= [2z²(z - 3)] / [z(z - 3)]

= 2z

2z² [ z - 3 ]
------------------ = 2
z [ z - 3 ]

(2z^3 - 6z^2) / (z^2 - 3z)
= 2z^2(z - 3) / z(z - 3)
= 2z

If that is:

(2z³ - 6z²) / (z² - 3z)

Then the first thing that I'll do is pull out the common factors. 2z² in the numerator and z in the denominator:

2z²(z - 3) / [z(z - 3)]

Now we can cancel out our common factors, z and (z - 3) to leave this as our answer:

2z