Mr Fantastic, Iappreciated your clear explanation with my other questions, and hope that you will help me with these too!really

I need to check my answers to these two questions:

simplify by dividing:

x^3+2x^2+3x-6/x-1{my answer was: x^2+3x+(6/x-1)}

n^3-27/n-3{my answer was n^2+3n-9}

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I'm having a bit trouble with this question:

the sum of a number and its reciprocal is 10/3. what is the number?

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I also need to make sure that my method is correct and the answer is sound, for this question.

One eighth of the square root of seven less than a number is two. What is the number?

My answer is 263. I came to this answer by working it backward, if 2*8=16, then 16*16=256 and 256+7=263. So if the equation version of the word problem was: (1/8)sqrtN-7=2 then the answer is: (2*8)^2+7=263

Finally, a little while back I posted the following question:

To which I got these two replies: