What is (24+5n-n^2)/(n^2-16n+64) ?

The solution to (24+5n-n^2)/(n^2-16n+64) is -(n+3)/(n-8)

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simplify (24+5n-n^2)/(n^2-16n+64)

simplify

\frac{24 + 5 n - n ^{2}}{n ^{2} - 16 n + 64}

- \frac{n + 3}{n - 8}

Solution steps

\frac{24 + 5 n - n ^{2}}{n ^{2} - 16 n + 64}

Factor

24 + 5 n - n^{2} : - (n + 3) (n - 8)

= \frac{- ( n + 3 ) ( n - 8 )}{n ^{2} - 16 n + 64}

Factor

n^{2} - 16 n + 64 : (n - 8)^{2}

= \frac{- ( n + 3 ) ( n - 8 )}{( n - 8 ) ^{2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(n - 8)^{2} = (n - 8) (n - 8)

= \frac{- ( n + 3 ) ( n - 8 )}{( n - 8 ) ( n - 8 )}

Cancel the common factor:

n - 8

= \frac{- ( n + 3 )}{n - 8}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{n + 3}{n - 8}

5^{2} \cdot 5^{5}

8 x - 6 y x^{2} + 1

x^{2} - 4 \geq 1

8 x^{2} - 10 = - 2

5^{- ∣ x ∣} = \frac{1}{25}

What is (24+5n-n^2)/(n^2-16n+64) ?
The solution to (24+5n-n^2)/(n^2-16n+64) is -(n+3)/(n-8)