# Thread: tangent slope of f

1. ## tangent slope of f

what is the tangent slope of the f(x)= $\displaystyle \frac{5}{x}$ at the point (-2, $\displaystyle \frac{-5}{2}$) using the formula lim x->a $\displaystyle \frac{f(x)-f(a)}{x-a}$
$\displaystyle \frac{\frac{5}{x}-(-\frac{5}{2})}{x-(-2)}$

i get two here and i am stuck
$\displaystyle \frac{\frac{5}{x}+(\frac{5}{2})}{x+2}$
I can see that I can potentially cancel out the (x+2)but I am not sure.

2. ## Re: tangent slope of f

Originally Posted by delgeezee
what is the tangent slope of the f(x)= $\displaystyle \frac{5}{x}$ at the point (-2, $\displaystyle \frac{-5}{2}$) using the formula lim x->a $\displaystyle \frac{f(x)-f(a)}{x-a}$
$\displaystyle \frac{\frac{5}{x}-(-\frac{5}{2})}{x-(-2)}$

i get two here and i am stuck
$\displaystyle \frac{\frac{5}{x}+(\frac{5}{2})}{x+2}$
I can see that I can potentially cancel out the (x+2)but I am not sure.
The next step is

$\displaystyle \frac{\frac{10+5x}{2x}}{x+2}$

3. ## Re: tangent slope of f

remember that (a/b)/c = (a/b)(1/c) = a/(bc), to simplify the fraction.

does x+2 divide 10+5x evenly?