Question

Which sum is equal to

Answer 1

Answer:

First choice: $\frac{1}{x+5}+\frac{x}{x-5}$

Step-by-step explanation:

Rather than factoring the original expression to match to the list of choices, in this case it is easier to add the terms in each choice and see if it can make up the original expression. Eye balling can exclude some options quickly.

Taking the first choice and adding the two terms:

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

Answer 2

Your answer should be a