These are some more problems of the same type that I got wrong in my newest lesson! I'll need the answers and your work for it.
I'm just here to get some help with an online math course I'm taking.
The latexing did not turn out well so we are going to need to put the problems in an understandable form.
I am guessing for the first one:
For the second one,
In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.
Clicking on your LaTex I think I can see what the problems look like:
1) (21x^3+14x)/7 = 21x^3/7 + 14x/7 = ?
2) (3(2x-3)-x(2x-3))/(2x-3) = 3(2x-3)/(2x-3) - x(2x-3)/(2x-3) = ?
3) ((x^2(5x+6)-3(5x+6))/(5x+6) = x^2(5x+6)/(5x+6) - 3(5x+6)/(5x+6) = ?
In each of these we are dividing the denominator into each of the two terms. Then in
each of these cancel to obtain the final answer.
Or you can take the original numerators and factor them and then cancel:
1) 7x(3x^2+2)/7 = ?
2) (2x-3)(3-x)/(2x-3) = ?
3) (5x+6)(x^2-3)/(5x+6) = ?
The first approach is probably easier.
Can you take them from here?
Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.