Question

Which sum is equal to

Answer 1

Answer:

Correct choice is A

Step-by-step explanation:

Note that the denominator $x^2-25=(x-5)(x+5).$ Then rewrite the numerator $x^2+6x-5$ as $x^2+5x+x-5=x(x+5)+(x-5).$

Substitute both expression into the initial expression:

$\dfrac{x^2+6x-5}{x^2-25}=\dfrac{x(x+5)+(x-5)}{(x+5)(x-5)}=\dfrac{x(x+5)}{(x+5)(x-5)}+\dfrac{(x-5)}{(x+5)(x-5)}=\dfrac{x}{x-5}+\dfrac{1}{x+5}.$