Simplify.
-$$\frac { ( x + 5 ) ^ { - 1 } + ( x - 5 ) ^ { - 1 } } { \left( x ^ { 2 } - 25 \right) ^ { - 1 } }$$
A) $2 x$
B) $- 10$
C) 10
D) $x ^ { 2 }$

Question

Quizplus · Accepted Answer

The given expression can be simplified by finding a common denominator for the numerator and recognizing that the denominator is already the difference of squares inverted. Simplifying, we get: $$\frac { ( x + 5 ) ^ { - 1 } + ( x - 5 ) ^ { - 1 } } { \left( x ^ { 2 } - 25 \right) ^ { - 1 } } = \frac { \frac { 1 } { x + 5 } + \frac { 1 } { x - 5 } } { \frac { 1 } { x ^ { 2 } - 25 } }$$ Multiplying both terms in the numerator by the other's denominator to get a common denominator gives: $$\frac { \frac { x - 5 + x + 5 } { x ^ { 2 } - 25 } } { \frac { 1 } { x ^ { 2 } - 25 } } = \frac { 2x } { x ^ { 2 } - 25 } \times \frac { x ^ { 2 } - 25 } { 1 }$$ The $x^2 - 25$ terms cancel out, leaving $2x$.

Simplify - (x+5)−1+(x−5)−1(x2−25)−1\frac { ( x + 5 ) ^ { - 1 } + ( x - 5 ) ^ { - 1 } } { \left( x ^ { 2 } - 25 \right) ^ { - 1 } }(x2−25)−1(x+5)−1+(x−5)−1​

Simplify
- $\frac { ( x + 5 ) ^ { - 1 } + ( x - 5 ) ^ { - 1 } } { \left( x ^ { 2 } - 25 \right) ^ { - 1 } }$