Solve the equation.
-$\frac { m + 8 } { m ^ { 2 } + 4 m + 3 } - \frac { 8 } { m ^ { 2 } + 6 m + 9 } = \frac { m - 8 } { m ^ { 2 } + 4 m + 3 }$
A) $\{ - 5 \}$
B) $\{ - 40 \}$
C) $\{ 5 \}$
D) $\{ - 8 \}$

Question

Quizplus · Accepted Answer

To solve the equation, first factor the denominators: $m^2 + 4m + 3 = (m + 1)(m + 3)$ and $m^2 + 6m + 9 = (m + 3)^2$. The equation becomes $\frac{m + 8}{(m + 1)(m + 3)} - \frac{8}{(m + 3)^2} = \frac{m - 8}{(m + 1)(m + 3)}$. Multiplying through by the common denominator $(m + 1)(m + 3)^2$ eliminates the fractions, leading to a solvable equation. Solving this equation correctly results in $m = -5$, which is option A.

Solve the Equation m+8m2+4m+3−8m2+6m+9=m−8m2+4m+3\frac { m + 8 } { m ^ { 2 } + 4 m + 3 } - \frac { 8 } { m ^ { 2 } + 6 m + 9 } = \frac { m - 8 } { m ^ { 2 } + 4 m + 3 }m2+4m+3m+8​−m2+6m+98​=m2+4m+3m−8​

Solve the Equation $\frac { m + 8 } { m ^ { 2 } + 4 m + 3 } - \frac { 8 } { m ^ { 2 } + 6 m + 9 } = \frac { m - 8 } { m ^ { 2 } + 4 m + 3 }$