Question

I don’t know what I’m doing please help!!

Answer 1

(n -13)/(n -7)

Explanation:

Simplify the fraction on the left, then add the two fractions.

`\displaystyle(n^2-10n+24)/(n^2-13n+42)-(9)/(n-7)=((n-6)(n-4))/((n-6)(n-7))-(9)/(n-7)\\\\=(n-4)/(n-7)-(9)/(n-7)\\\\=(n-4-9)/(n-7)\\\\=(n-13)/(n-7)`

_____

Comment on the graph

The vertical asymptote tells you the simplified form has one zero in the denominator at x=7. That is, the denominator is x-7.

The x-intercept at 13 tells you that x-13 is a factor of the numerator.

The horizontal asymptote at y=1 tells you there is no vertical scaling, so the simplest form is ...

(n -13)/(n -7)

The hole at x=6 is a result of the factor (x-6) that is cancelled from the first fraction in the original expression. At that value of x, the fraction is undefined. So, the above solution should come with the restriction x ≠ 6.