Solve the equation.
-$$\frac { x } { x - 6 } - \frac { 6 } { x + 6 } = \frac { 72 } { x ^ { 2 } - 36 }$$
A) $\varnothing$
B) $\{ \pm 6 \mathrm { i } \}$
C) $\{ \pm 6 \}$
D) $\left\{ \frac { 1 } { 6 } \right\}$

Question

Quizplus · Accepted Answer

The equation simplifies to an identity that is true for all x except the values that make the denominators zero, which are $x = 6$ and $x = -6$. However, these values are excluded from the solution set because they make the denominators zero, leading to division by zero, which is undefined. Therefore, the correct answer is $\varnothing$, indicating that there is no solution to the equation within the domain of real numbers.

Solve the Equation xx−6−6x+6=72x2−36\frac { x } { x - 6 } - \frac { 6 } { x + 6 } = \frac { 72 } { x ^ { 2 } - 36 }x−6x​−x+66​=x2−3672​

Solve the Equation $\frac { x } { x - 6 } - \frac { 6 } { x + 6 } = \frac { 72 } { x ^ { 2 } - 36 }$