Question

SIMPLIFY FRACTION

Answer 1

\[\frac{ \frac{ 1 }{ x }-\frac{ 1 }{ x+h } }{ h }\]

Answer 2

Please, you have to calculate the least common multiple between the two rational function, at the numerator

Answer 3

I actually done this, but I am not sure of answer, because WolframAlpha is saying something else.
My answer was \[\frac{ 1 }{ hx^2+hx }\]

Answer 4

Sorry, it is wrong: the right answer is:
\[h/(x ^{2}+hx)\]

Answer 5

can you tell me step by step how you done that?

Answer 6

I got \(\dfrac{1}{x^2+xh}\)? @Michele_Laino

Answer 7

Ah, I got same geerky, that hx^2 was missclick

Answer 8

Ok! I write all the steps:
\[1/x-1/(x+h)=(x+h-h)/(x ^{2}+hx)\]
because, the least common multiple is:
\[x(x+h)\]

Answer 9

@geerky42 you are right, that's the final result

Answer 10

\[
\begin{array}~
\dfrac{\dfrac{1}{x}-\dfrac{1}{x+h}}{h}&=\dfrac{\dfrac{x+h}{x(x+h)}-\dfrac{x}{x(x+h)}}{h}\\~\\&=\dfrac{\dfrac{h}{x(x+h)}}{h} \\~\\&=\dfrac{1}{x(x+h)}\\~\\ &=\boxed{\dfrac{1}{x^2+xh}}
\end{array}
\]

Answer 11

@Michalas I'm sorry there is an error, the right formula is:
\[1/x-1/(x+h)=(x+h-x)/(x(x+h))\]

Answer 12

Please, try to divide the above result, and you have the right answer!