Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$$\frac { 2 x } { x + 2 } + \frac { 5 } { x - 5 } = \frac { 8 } { x ^ { 2 } - 3 x - 10 }$$
A) $x = 2$
B) $x = \frac { 1 } { 2 }$ or $x = 2$
C) $x = \frac { 1 } { 4 }$ or $x = 4$
D) $x = - \frac { 1 } { 2 }$ or $x = 2$

Question

Quizplus · Accepted Answer

The equation is equivalent to:$$\frac { 2 x ( x - 5 ) } { ( x + 2 ) ( x - 5 ) } + \frac { 5 ( x + 2 ) } { ( x + 2 ) ( x - 5 ) } = \frac { 8 } { ( x + 2 ) ( x - 5 ) }$$$$2 x ( x - 5 ) + 5 ( x + 2 ) = 8$$$$2 x ^ { 2 } - 10 x + 5 x + 10 = 8$$$$2 x ^ { 2 } - 5 x + 2 = 0$$$$( 2 x - 1 ) ( x - 2 ) = 0$$$$x = \frac { 1 } { 2 } 	ext { or } x = 2$$

Choose the One Alternative That Best Completes the Statement or Answers