What is (n^2-12n+36)/(108-3n^2) ?

The solution to (n^2-12n+36)/(108-3n^2) is -(n-6)/(3(6+n))

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simplify (n^2-12n+36)/(108-3n^2)

simplify

\frac{n ^{2} - 12 n + 36}{108 - 3 n ^{2}}

- \frac{n - 6}{3 ( 6 + n )}

Solution steps

\frac{n ^{2} - 12 n + 36}{108 - 3 n ^{2}}

Factor

n^{2} - 12 n + 36 : (n - 6)^{2}

= \frac{( n - 6 ) ^{2}}{108 - 3 n ^{2}}

Factor

108 - 3 n^{2} : 3 (6 + n) (6 - n)

= \frac{( n - 6 ) ^{2}}{3 ( 6 + n ) ( 6 - n )}

3 (6 + n) (6 - n) = - 3 (6 + n) (n - 6)

= \frac{( n - 6 ) ^{2}}{- 3 ( 6 + n ) ( n - 6 )}

Apply exponent rule:

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

(n - 6)^{2} = (n - 6) (n - 6)

= \frac{( n - 6 ) ( n - 6 )}{- 3 ( 6 + n ) ( n - 6 )}

Cancel the common factor:

n - 6

= \frac{n - 6}{- 3 ( 6 + n )}

Apply the fraction rule:

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

= - \frac{n - 6}{3 ( 6 + n )}

3 x^{2} = 1 - 6 x

16 - 4 (4 - x) = 3 (1 - x)

36 x^{2} - 100

3 x < 18

2 (x - 3) (x + 5) = 0

What is (n^2-12n+36)/(108-3n^2) ?
The solution to (n^2-12n+36)/(108-3n^2) is -(n-6)/(3(6+n))