Which expression represents the sum of the following?
(3n / n^2 - 2n + 1) + (5 / n - 1)
a) 8n - 1 / (n - 1)^3
b) 8n - 5 / (n - 1)^3
c) 8n - 5 / (n - 1)^2
d) 8n - 1 / (n - 1)^2
b
If the posted expression is interpreted as is, none of the answer is correct.
The rules of priority of operations require that, in the absence of parentheses, multiplications and divisions are executed before additions and subtractions.
Therefore, whenever a numerator or denominator of a fraction is to be transcribed to a single line (as opposed to a typeset expression), parentheses must be inserted individually to the numerator and the denominator to indicate the extent of the numerator and denominator, unless they consist of a single term. If in doubt, insert parentheses anyway.
If your expression is
3n/(n^2-2n+1) + 5/(n-1)
answer (b) is not correct.
You will need to convert the expression to a common denominator
3n/(n^2-2n+1) + 5/(n-1)
=3n/(n-1)^2 + 5(n-1)/(n-1)^2
=(3n+5(n-1))/(n-1)^2
Can you take it from here?