Solve. Find all valid real roots for the equation.
-$$2 + \frac { 5 } { 5 x - 1 } = \frac { - 2 } { ( 5 x - 1 ) ^ { 2 } }$$
A) $x = - \frac { 1 } { 5 } , x = 0$
B) $x = - \frac { 1 } { 5 } , x = \frac { 1 } { 10 }$
C) $x = - 2 , x = - \frac { 1 } { 2 }$
D) $x = - \frac { 1 } { 5 } , x = - \frac { 1 } { 10 }$

Question

Quizplus · Accepted Answer

First, multiply both sides by $(5x - 1)^2$ to eliminate the denominators, resulting in a quadratic equation. Solving this quadratic equation yields $x = -\frac{1}{5}$ and $x = \frac{1}{10}$ as the valid real roots.

Solve Find All Valid Real Roots for the Equation 2+55x−1=−2(5x−1)22 + \frac { 5 } { 5 x - 1 } = \frac { - 2 } { ( 5 x - 1 ) ^ { 2 } }2+5x−15​=(5x−1)2−2​

Solve Find All Valid Real Roots for the Equation $2 + \frac { 5 } { 5 x - 1 } = \frac { - 2 } { ( 5 x - 1 ) ^ { 2 } }$