Solve the equation.
-$\frac { 8 } { y + 3 } - \frac { 6 } { y - 3 } = \frac { 12 } { y ^ { 2 } - 9 }$
A)27
B)-27
C)54
D) $\sqrt { 45 }$

Question

Quizplus · Accepted Answer

The equation can be simplified by noticing that $y^2 - 9$ is the difference of squares, factoring to $(y + 3)(y - 3)$. Thus, the equation can be rewritten with a common denominator:$$\frac{8}{y + 3} - \frac{6}{y - 3} = \frac{12}{(y + 3)(y - 3)}$$Multiplying both sides by $(y + 3)(y - 3)$ to eliminate the denominators gives:$$8(y - 3) - 6(y + 3) = 12$$Expanding both sides:$$8y - 24 - 6y - 18 = 12$$Simplifying:$$2y - 42 = 12$$Adding 42 to both sides:$$2y = 54$$Dividing by 2:$$y = 27$$Therefore, the solution is $y = 27$.

Solve the Equation 8y+3−6y−3=12y2−9\frac { 8 } { y + 3 } - \frac { 6 } { y - 3 } = \frac { 12 } { y ^ { 2 } - 9 }y+38​−y−36​=y2−912​

Solve the Equation $\frac { 8 } { y + 3 } - \frac { 6 } { y - 3 } = \frac { 12 } { y ^ { 2 } - 9 }$