What is the largest positive integer n such that $\frac{n^2 + 7n + 12}{n^2 - n - 12}$ is also a positive integer?
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Question

What is the largest positive integer n such that $$\frac{n^2 + 7n + 12}{n^2 - n - 12}$$ is also a positive integer?

Accepted Answer

12. n 2 + 3 n + 4 n + 12 n 2 − 4 n + 3 n − 12 \ \frac{\ n^2+3n+4n+12}{n^2-4n+3n-12} n 2 − 4 n + 3 n − 12 n 2 + 3 n + 4 n + 12 ​ = n ( n + 3 ) + 4 ( n + 3 ) n ( n − 4 ) + 3 ( n − 4 ) \ \frac{\ n^{ }\left(n+3\right)+4\left(n+3\right)}{n^{ }\left(n-4\right)+3\left(n-4\right)} n ( n − 4 ) + 3 ( n − 4 ) n (

What is the largest positive integer n such that n2+7n+12n2−n−12\frac{n^2 + 7n + 12}{n^2 - n - 12}n2−n−12n2+7n+12​ is also a positive integer?

What is the largest positive integer n such that n2+7n+12n2−n−12\frac{n^2 + 7n + 12}{n^2 - n - 12}n2−n−12n2+7n+12​ is also a positive integer?

What is the largest positive integer n such that $\frac{n^2 + 7n + 12}{n^2 - n - 12}$ is also a positive integer?

What is the largest positive integer n such that $\frac{n^2 + 7n + 12}{n^2 - n - 12}$ is also a positive integer?