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uysha [10]
3 years ago
8

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

Mathematics
1 answer:
elixir [45]3 years ago
5 0

Answer:

  (n -13)/(n -7)

Step-by-step explanation:

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

\displaystyle\frac{n^2-10n+24}{n^2-13n+42}-\frac{9}{n-7}=\frac{(n-6)(n-4)}{(n-6)(n-7)}-\frac{9}{n-7}\\\\=\frac{n-4}{n-7}-\frac{9}{n-7}\\\\=\frac{n-4-9}{n-7}\\\\=\frac{n-13}{n-7}

_____

<em>Comment on the graph</em>

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.

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