Solve the equation.
-$\frac { m + 6 } { m ^ { 2 } + 10 m + 25 } - \frac { 6 } { m ^ { 2 } + 10 m + 25 } = \frac { m - 6 } { m ^ { 2 } + 10 m + 25 }$
A)-5
B)5
C)-30
D)no solution

Question

Quizplus · Accepted Answer

The equation simplifies to $\frac{m + 6 - 6}{m^2 + 10m + 25} = \frac{m - 6}{m^2 + 10m + 25}$, which simplifies to $\frac{m}{m^2 + 10m + 25} = \frac{m - 6}{m^2 + 10m + 25}$. This implies $m = m - 6$, leading to $0 = -6$, which is not possible. However, the simplification shows that the equation holds for $m = -5$ because the denominator becomes zero, indicating a removable discontinuity.

Solve the Equation m+6m2+10m+25−6m2+10m+25=m−6m2+10m+25\frac { m + 6 } { m ^ { 2 } + 10 m + 25 } - \frac { 6 } { m ^ { 2 } + 10 m + 25 } = \frac { m - 6 } { m ^ { 2 } + 10 m + 25 }m2+10m+25m+6​−m2+10m+256​=m2+10m+25m−6​

Solve the Equation $\frac { m + 6 } { m ^ { 2 } + 10 m + 25 } - \frac { 6 } { m ^ { 2 } + 10 m + 25 } = \frac { m - 6 } { m ^ { 2 } + 10 m + 25 }$