## osanseviero one year ago A function operation

1. osanseviero

if $F(x)=\frac{ 1 }{ x }$ find and express its simplest form: $\frac{ f(a+h)-f(a) }{ h }$

2. osanseviero

That's all I have, what should I do?

3. Easyaspi314

You should get -1/ (a(a+h))

4. osanseviero

$(\frac{ 1 }{ a+h }-\frac{ 1 }{ a }) \div h$

5. osanseviero

Like that?

6. Easyaspi314

I'll start you off.......... Given: f(x) = 1/x So, f(a+h) = 1/(a+h) and f(a) = 1/a So the expression you typed above is just: [ (1/(a+h) - 1/a] /h When you simplify that complex fraction above (not hard at all), you get -1/[a(a+h)] as your final answer.

7. Easyaspi314

Yes, like that!

8. osanseviero

Can you explain how did you simplify, please?

9. Easyaspi314

Let's take the numerator........ 1/(a+h) - 1/a To subtract, you get the LCD which is a(a+h), so 1/(a+h) - 1/a = [a-(a+h)]/a(a+h) = -h/(a(a+h)) Now, the denominator is just h, so you get -h/(a(a+h)) divided by h/1 = -1/(a(a+h))

10. Easyaspi314

makes sense?

11. osanseviero

yep, thanks

12. Easyaspi314

welcome.

13. osanseviero

I had a silly math confusion