1.

What is the largest positive integer such that \(\frac{n^2 + 7n + 12}{n^2 - n - 12}\) also a positive integer?1. 62. 163. 124. 8

Answer» Correct Answer - Option 3 : 12

Calculation:

\(\frac{n^2 + 7n + 12}{n^2 - n - 12}\)

⇒ \(\frac{{{n^2} + 3n + 4n + 12}}{{{n^2}\;- 4n + 3n + 12}}\)

⇒ \(\frac{{n\left( {n + 3} \right) + 4\left( {n + 3} \right)}}{{n\left( {n - 4} \right) + 3\left( {n - 4} \right)}}\)

⇒ \(\frac{{\left( {n + 3} \right)\left( {n + 4} \right)}}{{\left( {n - 4} \right)\left( {n + 3} \right)}}\)

⇒ \(\frac{{\left( {n + 4} \right)}}{{\left( {n - 4} \right)}}\)

⇒ \(\frac{{\left( {n - 4 + 4 + 4} \right)}}{{\left( {n - 4} \right)}}\)

⇒ \(1 + \;\frac{8}{{\left( {n - 4} \right)}}\)

Which will be maximum when (n - 4 = 8)

So, n = 12

∴ The largest positive integer is 12.


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