SOLUTION: state the excluded values for the following expression. then simplify the expression. (10n-90)/n^2-17n+72

Algebra ->  Expressions-with-variables -> SOLUTION: state the excluded values for the following expression. then simplify the expression. (10n-90)/n^2-17n+72      Log On


   

Question 1121190: state the excluded values for the following expression. then simplify the expression.
(10n-90)/n^2-17n+72
Found 3 solutions by josgarithmetic, ikleyn, rothauserc:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Are you trying to show %2810n-90%29%2F%28n%5E2-17n%2B72%29?
(Use parentheses where needed!)

%2810n-90%29%2F%28%28n-8%29%28n-9%29%29

%2810%28n-9%29%29%2F%28%28n-8%29%28n-9%29%29
Now the excluded values of n should be obvious.

Answer by ikleyn(52806) About Me  (Show Source):
You can put this solution on YOUR website!
.
The excluded values are those where the denominator becomes equal to zero.


They are the root of the equation


n^2 - 17n + 72 = 0.


Factor left side quadratic polynomial to get the roots:


(n-9)*(n-8) = 0.


The roots are  n= 8  and  n= 9.


So, the excluded values are  8 and 9.


Then the expression is


%2810n-90%29%2F%28n%5E2-17n+%2B+72%29 = %2810%2A%28n-9%29%29%2F%28%28n-9%29%2A%28n-8%29%29 = cancel the factors (n-9) in the numerator and in the denominator = 10%2F%28n-8%29.

Completed and solved.


Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
10n-90/n^2-17n+72
:
n = 9, n = 8 are the excluded values
:
10(n-9)/(n-9)(n-8) = 10/(n-8)
:
Note in the simplified form, the excluded value is n=8
: