1. ## Difference Quotient

Find the difference quotient of f, that is, find [f(x + h) - f(x)]/h, where h cannot = 0, for the given function.

Be sure to simplify.

f(x) = 1/(x + 3)

NOTE: This question comes from a precalculus textbook and so the explanation must be in precalculus terms and NOT calculus.

2. Hello,

Originally Posted by magentarita
Find the difference quotient of f, that is, find [f(x + h) - f(x)]/h, where h cannot = 0, for the given function.

Be sure to simplify.

f(x) = 1/(x + 3)

NOTE: This question comes from a precalculus textbook and so the explanation must be in precalculus terms and NOT calculus.
Hmmm well, this doesn't involve calculus, only algebra

$f(x+h)=\frac{1}{(x+h)+3}$

So $\frac{f(x+h)-f(x)}{h}=\frac{\frac{1}{x+h+3}-\frac{1}{x+3}}{h}$

Now, get the common denominator of the numerator and put it on the same fraction.

Remember : $\frac ab+\frac cd=\frac{ad}{bd}+\frac{cb}{bd}=\frac{ad+bc}{bd}$

Can you finish ?

3. ## Yes..I can

Yes, I can finish now.

I got stuck in terms of the value of x in the fraction 1/(x + 3).

I did not see that x = (x + h).

Thanks