Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$$\frac { 2 z } { z - 2 } + \frac { 3 } { z - 4 } = 1$$
A) $\left\{ - \frac { 1 } { 2 } \pm \frac { \sqrt { 57 } } { 2 } i \right\}$
B) $\left\{ - \frac { 1 } { 2 } \pm \frac { \sqrt { 57 } } { 2 } \right\}$
C) $\left\{ \frac { 1 } { 2 } \pm \frac { \sqrt { 57 } } { 2 } i \right\}$
D) $\left\{ \frac { 1 } { 2 } \pm \frac { \sqrt { 57 } } { 2 } \right\}$

Question

Quizplus · Accepted Answer

To solve the equation $\frac { 2 z } { z - 2 } + \frac { 3 } { z - 4 } = 1$, we first find a common denominator, which is $(z-2)(z-4)$, and rewrite the equation accordingly. After simplifying and moving all terms to one side, we get a quadratic equation. Solving this quadratic equation using the quadratic formula gives us the roots $\left\{ - \frac { 1 } { 2 } \pm \frac { \sqrt { 57 } } { 2 } \right\}$, indicating that choice B is correct.

Choose the One Alternative That Best Completes the Statement or Answers