I guess she must have made a mistake, although everything still works together to the same end result...I can see she must have been explaining a "concept" to someone, as she had underlined the "-10t", "+3t" and "-t"....
anycase, I'm putting this to bed now...CPill, you were a great help!!..thanx a lot!!
Well your approach I like....I had a look and saw that you "carried" everything over to the left side in steps, and ended with:
-1 (t - 1)(t - 3) on the right side later on..
then all of that became -t^2 +4t -3..which I perfectly understand...
I was hoping to get a reasoning behind the calculation the teacher had done here;
= -10 (t - 1) - (t - 1)(t - 3) + 5 became -10t + 10 - t^2 + 3t - t - 3 + 5...
I do not understand the rule or law to change the signs like that...
I would have written:
= -10 (t - 1) - (t^2 - 3t - t + 3)..which would then become
= - 10 (t - 1) - t^2 + 3t + t - 3..which is EXACTLY what you also got..how did she get "- t" ?
I can see on the paper she used pencil to indicate she was changing the sign of the second t to a "-" inside the bracket, and the "-1" to a "+1" in this part of the sum: = -10 (t - 1) - (t - 1)(t - 3) + 5...why did she do that?...and how would this give the "-t" in any case?...I followed her calculations from thereon and everything calculates to the same end result...
the left side I also got, however this is what I did with the right side:
\(18x^3 \over x(9x^2+1)-3(9x^2+1)\)
\(18x^3 \over (x-3)(9x^2+1)\)
\(18x^2 \over (x-3)(3x+1)(3x+1)\)
so now it's;
and this is where it ends for me...yes, I do not know, either = or * would have worked nicely, but subtraction?..I don't know..
Melody, anyways, thank you kindly once again for your help...I think I'll let this one pass..