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Using the intergarting rules, you would add a power then divide that new number to the coefficent so you would get 5x^3 and just add one x to the 7 and dont forget the c. So the end answer would be 5x^3 +...

We are searching for a rule that when we put in n (n represetning where the term is in the sequence eg. 3 is the first term so n will be 1) our output is the sequence above. This rule will most likely be ...

5x - 2 < 3x + 11 --> 5x < 3x + 13 (Add 2) --> 2x < 13 (Subtract 3x) --> x < 13/2 (Divide by 2)

log_{x} (7y+1) - log{x} (2y) =1 --> log_{x} [(7y+1)/2y]=1 (y =/= 0, Rules of logarithms i.e. difference of logarithms) --> x = [(7y+1)/2y] (x>0, Rules of logarithms i.e. log_{x} x = 1) --> 2yx...

A/(x-2) + B/(x+1) + C/(x+1)^2