First, write the value(s) that make the denominator(s) zero. Then solve the equation.
-$$\frac { m + 3 } { m ^ { 2 } - 2 m - 8 } - \frac { 3 } { m ^ { 2 } + 4 m + 4 } = \frac { m - 3 } { m ^ { 2 } - 2 m - 8 }$$
A) $\{ - 8 \}$
B) $\{ - 24 \}$
C) $\{ 8 \}$
D) $\{ - 30 \}$ Find all values of x satisfying the given conditions.

Question

Quizplus · Accepted Answer

To find the values that make the denominators zero, we factor each denominator. The first and third denominators are the same: $m^2 - 2m - 8$, which factors to $(m - 4)(m + 2)$, giving roots $m = 4$ and $m = -2$. The second denominator is $m^2 + 4m + 4$, which factors to $(m + 2)^2$, giving a root $m = -2$. Thus, the values that make the denominators zero are $m = 4$ and $m = -2$, but these are not the solutions to the equation; they are values to be excluded from the solution set. To solve the equation, we first find a common denominator, which is $(m - 4)(m + 2)^2$. After simplifying and solving the equation, we find that there are no solutions because the equation simplifies to an identity that does not hold for any value of $m$. The initial question seems to have been misunderstood, as it asks for the values that make the denominators zero, not the solution to the equation. The correct answer should reflect the values that cannot be used, which are $m = 4$ and $m = -2$, but these are not among the provided options, indicating a possible mistake in interpreting the question or in the provided options.

First, Write the Value(s) That Make the Denominator(s) Zero m+3m2−2m−8−3m2+4m+4=m−3m2−2m−8\frac { m + 3 } { m ^ { 2 } - 2 m - 8 } - \frac { 3 } { m ^ { 2 } + 4 m + 4 } = \frac { m - 3 } { m ^ { 2 } - 2 m - 8 }m2−2m−8m+3​−m2+4m+43​=m2−2m−8m−3​

First, Write the Value(s) That Make the Denominator(s) Zero $\frac { m + 3 } { m ^ { 2 } - 2 m - 8 } - \frac { 3 } { m ^ { 2 } + 4 m + 4 } = \frac { m - 3 } { m ^ { 2 } - 2 m - 8 }$