Consider the function below.

Evaluate the difference quotient for the given function. Simplify your answer.

and here is my attempt

$\displaystyle (((x+7)/(x+5))-((5+7)/(5+5)))/x-5$

first, I just did the math

$\displaystyle

(((x+7)/(x+5))-(6/5))/x-5$

then the only thing I could think of was to do me some rationalizing

$\displaystyle (-6(x+5)+5(x+7))/(5(x+5)(x-5))$

and some nice little simplification

$\displaystyle (5-x)/(5x^2 -125)$

I have a sneaky notion that this is incorrect.