Solve the proportion. $\frac { n ^ { 2 } } { 6 } = \frac { n } { n + 1 }$
A) $n = - 2 , n = 1 , n = 3$
B) $n = - 4 , n = - 1 , n = 1$
C) $n = - 3 , n = 0 , n = 2$
D) $n = - 5 , n = - 2 , n = 0$
E) no solution

Question

Quizplus · Accepted Answer

To solve the proportion, cross-multiply to get $n^2(n+1) = 6n$. Simplifying gives $n^3 + n^2 - 6n = 0$. Factoring out $n$, we have $n(n^2 + n - 6) = 0$. Further factoring gives $n(n-2)(n+3) = 0$, leading to solutions $n = 0, n = 2, n = -3$.

Solve the Proportion n26=nn+1\frac { n ^ { 2 } } { 6 } = \frac { n } { n + 1 }6n2​=n+1n​

Solve the Proportion $\frac { n ^ { 2 } } { 6 } = \frac { n } { n + 1 }$