Make an appropriate substitution and solve the equation.
-$$\frac { 3 } { ( n + 4 ) ^ { 2 } } - \frac { 1 } { n + 4 } = 4$$
A) $\left\{ - 5 , - \frac { 13 } { 4 } \right\}$
B) $\left\{ - 1 , \frac { 4 } { 3 } \right\}$
C) $\left\{ - 5 , \frac { 4 } { 3 } \right\}$
D) $\left\{ - 1 , \frac { 19 } { 3 } \right\}$

Question

Quizplus · Accepted Answer

By substituting $u = n + 4$, the equation becomes $\frac{3}{u^2} - \frac{1}{u} = 4$. Multiplying through by $u^2$ gives a quadratic equation in $u$, which can be solved to find the values of $n$ corresponding to the choices given.

Make an Appropriate Substitution and Solve the Equation 3(n+4)2−1n+4=4\frac { 3 } { ( n + 4 ) ^ { 2 } } - \frac { 1 } { n + 4 } = 4(n+4)23​−n+41​=4

Make an Appropriate Substitution and Solve the Equation $\frac { 3 } { ( n + 4 ) ^ { 2 } } - \frac { 1 } { n + 4 } = 4$