Solve: $\frac { x } { 3 } - \frac { 7 } { 3 } = \frac { 6 } { x }$
A) $\{ - 2,9 \}$
B) $\{ - 9,2 \}$
C) $\left\{ - \frac { 9 } { 5 } \right\}$
D) $\left\{ \frac { 9 } { 5 } \right\}$

Question

Quizplus · Accepted Answer

To solve the equation $\frac{x}{3} - \frac{7}{3} = \frac{6}{x}$, we first eliminate the denominators by multiplying the entire equation by $3x$, which gives us $x^2 - 7x = 18$. Rearranging the equation to bring all terms to one side gives us $x^2 - 7x - 18 = 0$. Factoring this quadratic equation, we find $(x - 9)(x + 2) = 0$, which gives us the solutions $x = 9$ and $x = -2$. Therefore, the correct answer is $\{-2, 9\}$.

Solve x3−73=6x\frac { x } { 3 } - \frac { 7 } { 3 } = \frac { 6 } { x }3x​−37​=x6​

Solve $\frac { x } { 3 } - \frac { 7 } { 3 } = \frac { 6 } { x }$