wanted to see what someone else got for this

Please, when you post questions like this you need to use brackets!

CPhill has 'guessed' what you want!  I am sure he has guessed correctly but it is NOT what you asked for.

This is what you asked for

3t^2-11t+6/3t^2+7t-(6 divided by 9t^2)-12t+4/3t^2/3t^2+7t-6

This is what CPhill answered

(3t^2-11t+6/3t^2+7t-6) divided by (9t^2-12t+4/3t^2/3t^2+7t-6)

 THEY ARE DIFFERENT!!!!!

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When we divide, the 3t^2 +7t - 6 terms "cancel" with each other, so we're left with

(3t^2 - 11t + 6) / (9t^2 - 12t + 4)      Factoring, we have

[(3t - 2)(t - 3)] / [(3t -2)(3t - 2)]     And we're left with

(t - 3) / (3t - 2)