(x-3) (7x^2 +x +8)
x-3 / 7x^2 +x +8
???
What are you doing? (x-3) (7x^2 +x +8) indicates multiplication between the binomial and the trinomial. x-3 / 7x^2 +x +8 indicates division of -3 by 7. If you want to show division of the binomial by the trinomial you must use parentheses, also called grouping symbols: (x-3) /(7x^2 +x +8).
Please start using subject descriptions that are descriptive of each problem, not just " intermediate algebra" all the time.
Please study other posts to understand proper notation in order to convey information accurately.
No. x/(7x^2) does not equal 7x. When numbers or variables are being canceled, they do not just "disappear." They are replaced by "1". Also, things do not suddenly move from the denominator to the numerator. x/(7x^2) = 1/(7x).
Here is a little short cut you can use to check your work in problems like this. Replace x with some arbitrary number, say 10 (but make sure you don't pick a number that makes the denominator equal zero). Then find the value of the starting problem and check against the value of your solution. Example:
(x-3) /(7x^2 +x +8) = (10-3) /(7(10)^2 +10 +8) = 7/718
-3x +8 = -3(10) + 8 = -30 + 8 = -22
In this check, we see that the answers are not the same. Therefore we know that (x-3) /(7x^2 +x +8) does not equal -3x + 8.
Always check your answers.