Given g(x)=7/x + 3 , evaluate and simplify: g(2+h)−g(2)/h=

Question

Given g(x)=7/x+3, evaluate and simplify:

g(2+h)−g(2) =

h

Answer 1

g(x)=7 / (x+3)

want

(g(2+h) - g(2))/ h

First determine what the function g(x) evaluated at x=2+h is and at x=2 is.

substitute those into what you’re looking for and simplify.

im going to submit this so you can work on it with me. When I get my answer typed up I’ll resubmit so you can check against your findings.

***************

g(2+h) = 7 /((2+h)+3) = 7 /(h+5)

g(2) = 7 / (2+3) = 7/5

substitute these into what you’re looking for

(7/(h+5) - 7/5)/(h/1)

I went ahead and divided h by 1 to show this was a complex fraction made up of three fractions being 7/(h+5) , 7/5 and h/1. Notice the lcd of these fractions is 5(h+5). So multiply every fraction making up the complex fraction (those listed) by 5(h+5). This converts the complex fraction into the normal (but still needing to be simplified) fraction below

(5*7 -7(h+5)) / (h*5(h+5))

= (35 -7h - 35) / (5h(h+5))

= (- 7h) / (5h(h+5)).

=-7 / (5(h+5)).