1. horray for difference quotients

Consider the function below.

and here is my attempt
$(((x+7)/(x+5))-((5+7)/(5+5)))/x-5$

first, I just did the math

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

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

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

and some nice little simplification

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

I have a sneaky notion that this is incorrect.

2. Hello,
Originally Posted by leftyguitarjoe
$(-6(x+5)+5(x+7))/(5(x+5)(x-5))$

and some nice little simplification

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

I have a sneaky notion that this is incorrect.
Nope, this is correct !
But you should have stayed at this step :
$\frac{-6(x+5)+5(x+7)}{5(x+5)(x-5)}$

Don't expand the denominator yet and calculate the numerator