Solve.
-$$3 = - \frac { 8 } { x } - \frac { 1 } { x ^ { 2 } }$$
A) $\frac { - 4 \pm \sqrt { 19 } } { 3 }$
B) $\frac { - 4 \pm \sqrt { 13 } } { 3 }$
C) $\frac { - 4 \pm \sqrt { 13 } } { 6 }$
D) $\frac { - 8 \pm \sqrt { 13 } } { 3 }$

Question

Quizplus · Accepted Answer

To solve the equation $3 = - \frac { 8 } { x } - \frac { 1 } { x ^ { 2 } }$, multiply both sides by $x^2$ to eliminate the denominators, resulting in a quadratic equation: $3x^2 + 8x + 1 = 0$. Using the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = 3$, $b = 8$, and $c = 1$, we find $x = \frac{-8 \pm \sqrt{64 - 12}}{6} = \frac{-8 \pm \sqrt{52}}{6} = \frac{-8 \pm 2\sqrt{13}}{6} = \frac{-4 \pm \sqrt{13}}{3}$, which matches choice B.

Solve - 3=−8x−1x23 = - \frac { 8 } { x } - \frac { 1 } { x ^ { 2 } }3=−x8​−x21​

Solve
- $3 = - \frac { 8 } { x } - \frac { 1 } { x ^ { 2 } }$