1/h(x+h)^2
1/hx^2
What would you do to make the above rationals NOT be over 1?
There is no other question. I just want to make what I listed to not be over 1.
The original equation that I am solving is:
((1/h(x+h)^2)-(1/hx^2)) / h
I just wanted to make those two parts in the numerator a little bit more simpler so that they are not fractions. How do I go about doing so? Or is there some other way I can solve.
your difference quotient should be ...
$\displaystyle \frac{\frac{1}{(x+h)^2} - \frac{1}{x^2}}{h}$
it can be rewritten as ...
$\displaystyle \frac{1}{h}\left(\frac{1}{(x+h)^2} - \frac{1}{x^2}\right)$
work inside to get a common denominator ...
$\displaystyle \frac{1}{h}\left(\frac{x^2 - (x+h)^2}{x^2(x+h)^2}\right)$
expand the numerator ...
$\displaystyle \frac{1}{h}\left(\frac{x^2 - (x^2+2xh+h^2)}{x^2(x+h)^2}\right)$
combine like terms in the numerator ...
$\displaystyle \frac{1}{h}\left(\frac{-2xh-h^2)}{x^2(x+h)^2}\right)$
factor $\displaystyle -h$ out of the numerator ...
$\displaystyle \frac{1}{h}\left(\frac{-h(2x+h)}{x^2(x+h)^2}\right)$
divide out the h's ...
$\displaystyle \frac{-(2x+h)}{x^2(x+h)^2}$
if you have covered limits in class, take the limit as $\displaystyle h \to 0$ and simplify ...