Perform the indicated operation. $\frac { 7 n } { n ^ { 2 } - 25 } - \frac { 5 } { 2 n - 10 }$
A) $\frac { 9 n - 25 } { ( n + 5 ) ( n - 5 ) }$
B) $\frac { 9 n + 25 } { 2 ( n + 5 ) ( n - 5 ) }$
C) $\frac { 9 n + 25 } { ( n + 5 ) ( n - 5 ) }$
D) $\frac { 9 n - 25 } { 2 ( n + 5 ) ( n - 5 ) }$

Question

Quizplus · Accepted Answer

To add or subtract rational expressions, we need to find a common denominator. Factoring the denominators, we get:
$$\frac{7n}{n^2-25} - \frac{5}{2n-10} = \frac{7n}{(n-5)(n+5)} - \frac{5}{2(n-5)} = \frac{14n}{2(n-5)(n+5)} - \frac{5(n+5)}{2(n-5)(n+5)}$$
Combining the fractions, we get:
$$\frac{14n - 5n - 25}{2(n-5)(n+5)} = \frac{9n-25}{2(n-5)(n+5)}$$
Therefore, the correct answer is (D).

Perform the Indicated Operation 7nn2−25−52n−10\frac { 7 n } { n ^ { 2 } - 25 } - \frac { 5 } { 2 n - 10 }n2−257n​−2n−105​

Perform the Indicated Operation $\frac { 7 n } { n ^ { 2 } - 25 } - \frac { 5 } { 2 n - 10 }$