What is (n^2-225)/(n^2+30n+225) ?

The solution to (n^2-225)/(n^2+30n+225) is (n-15)/(n+15)

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simplify (n^2-225)/(n^2+30n+225)

simplify

\frac{n ^{2} - 225}{n ^{2} + 30 n + 225}

\frac{n - 15}{n + 15}

Solution steps

\frac{n ^{2} - 225}{n ^{2} + 30 n + 225}

Factor

n^{2} - 225 : (n + 15) (n - 15)

= \frac{( n + 15 ) ( n - 15 )}{n ^{2} + 30 n + 225}

Factor

n^{2} + 30 n + 225 : (n + 15)^{2}

= \frac{( n + 15 ) ( n - 15 )}{( n + 15 ) ^{2}}

Apply exponent rule:

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

(n + 15)^{2} = (n + 15) (n + 15)

= \frac{( n + 15 ) ( n - 15 )}{( n + 15 ) ( n + 15 )}

Cancel the common factor:

n + 15

= \frac{n - 15}{n + 15}

(\frac{y ^{2}}{y ^{\frac{4}{5}}})^{\frac{1}{3}}

x^{8} - 16 x^{4}

2 x^{3} \cdot x^{2}

x^{2} + 20 x + 36

What is (n^2-225)/(n^2+30n+225) ?
The solution to (n^2-225)/(n^2+30n+225) is (n-15)/(n+15)