Solve the equation.
-$\frac{9}{m-2}-\frac{6}{m+2}=\frac{6}{m^{2}-4}$
A) -8
B) $\sqrt{52}$
C) -24
D) 8

Question

Quizplus · Accepted Answer

The equation can be simplified by finding a common denominator, which is $m^2 - 4$ (since $m^2 - 4 = (m-2)(m+2)$). The equation becomes $\frac{9(m+2) - 6(m-2)}{m^2 - 4} = \frac{6}{m^2 - 4}$. Simplifying the numerator on the left side gives $\frac{9m + 18 - 6m + 12}{m^2 - 4} = \frac{6}{m^2 - 4}$, which simplifies further to $\frac{3m + 30}{m^2 - 4} = \frac{6}{m^2 - 4}$. Multiplying both sides by $m^2 - 4$ to eliminate the denominator gives $3m + 30 = 6$. Solving for $m$, we get $3m = -24$, so $m = -8$.

Solve the Equation 9m−2−6m+2=6m2−4\frac{9}{m-2}-\frac{6}{m+2}=\frac{6}{m^{2}-4}m−29​−m+26​=m2−46​ A) -8 B) 52\sqrt{52}52​ C) -24 D) 8

Solve the Equation $\frac{9}{m-2}-\frac{6}{m+2}=\frac{6}{m^{2}-4}$ A) -8
B) $\sqrt{52}$ C) -24
D) 8