Solve the equation. $n - \frac { 15 } { n } = \frac { 103 } { 6 }$
A) $\left\{ - \frac { 7 } { 6 } , 18 \right\}$
B) $\left\{ - \frac { 5 } { 6 } \right\}$
C) $\{ 18 \}$
D) $\left\{ - \frac { 7 } { 6 } \right\}$
E) $\left\{ - \frac { 5 } { 6 } , 18 \right\}$

Question

Quizplus · Accepted Answer

We multiply both sides by 6n to get rid of the fraction: $6n^2-15n=103n$. Simplifying gives $6n^2-118n=0$, which factors as $2n(3n-59)=0$. Thus, $n=\frac{59}{3}$ or $n=0$. However, if $n=0$, then we are dividing by zero in the original equation, so $n=\frac{59}{3}$. Plugging this back into the original equation, we see that it works. Thus, the solutions are $\left\{-\frac{5}{6},18ight\}$, so the answer is $\boxed{	extbf{(E)}}$.

Solve the Equation n−15n=1036n - \frac { 15 } { n } = \frac { 103 } { 6 }n−n15​=6103​

Solve the Equation $n - \frac { 15 } { n } = \frac { 103 } { 6 }$