How would I solve this problem?

Question

If g(x) = 1/x, what is the value of the expression g(x + h) – g(x)? Explanations would be wonderful!

Answer 1

g(x) = 1/x
g(x + h) = 1 / (x + h)

g(x-h) - g(x)

= 1/(x-h) - 1/x

Find a common denominator of x(x-h) for each term. Multiply the first term by (x/x); multiply the second term by (x-h)/(x-h).
= x / x(x-h) - (x-h) / x(x-h)

Simplify equation over common denominator
= [x - (x-h)] / x(x-h)

Subtract numerator
= h / x(x-h)

Answer 2

= 1/(x+h) - 1/x
= x/(x(x+h)) - (x+h)/(x(x+h))
= -h/[x(x+h)]

Answer 3

g(x) is equal to 1/x
so g(x+h) = 1/(x+h)
therefore g(x+h) - g(x) = [1/(x+h)] - [1/x]
= [x/x(x+h)] - [(x+h)/x(x+h)]
= (x-x-h)/x(x+h)
= -h/x(x+h)
= -h/x^2+xh

the trick is to substitute the x in the function with whatever inside the parantheses (in this case 1/x bacame 1/x+h which came from g(x+h)). After you do this, the rest is donr normally.
Good luck :)

Answer 4

g(x+h)-g(x) = (1/(x+h)) - (1/x)
=(x - (x+h))/(x^2-xh)
= - h/(x^2-xh)

Just change the denominator with x+h to get g(x+h)=1/(x+h), then subtract g(x) = 1/x.
Simplify the rational expression to come up with the final expression.

Answer 5

don't ask that during the summer, i just finished algebra and i really don't feel like doing it. haha.

Answer 6

g(x=1/x
g(x+h)=1/x+h
g(x+h)-g(x=1/(x+h)-1/x=-x-x-h/x(x+h).=-h/x(x+h).

Answer 7

-h/[x(x+h)]