Question

PLEASE HELP
Will award medal and fan for an explanation to this question! Question in comments (Involves simplifying (f(x-h)-f(x))/h

Answer 1

Given
\[f(x)=-3x+\frac{ 1 }{ x }-3 \]
Simplify
\[\frac{ f(x-h)-f(x) }{ h }\]
When x=4

Answer 2

what are u looking for

Answer 3

I just need to simplify (f(x-h)-f(x))/h when x=4

Answer 4

another way to write \[-3x+\frac{ 1 }{ x }-3\] is \[\frac{ -3x ^{2}-3x+1 }{ x }\] so then f(x+h) is \[\frac{ -3(x+h)^{2}-3(x+h)+1 }{ x+h }\] and then f(x+h)-f(x) is \[\frac{ -3(x ^{2}+2xh+h ^{2})-3x-3h+1 }{ x+h }-\frac{ -3x ^{2}-3x+1 }{ x }\] and then I give them the same denominator so that I can combine them\[\frac{ -3x ^{3}-6x ^{2}h-3xh ^{2}-3x ^{2}-3xh+x }{ x(x+h) }+\frac{ (x+h)(3x ^{2}+3x-1) }{ x(x+h) }\]and then multiply the numerator of the second part\[\frac{ 3x ^{3}+3x ^{2}h+3x ^{2}+3xh-x-h }{ x(x+h) }\]
and then cancel out as much as i can\[\frac{ -3x ^{2}h-3xh ^{2}-h }{ x(x+h) }\]and then I take an h out of the numerator\[\frac{ h(3x ^{2}-3xh-1) }{ x(x+h) }\] so basically my question is: how to I simplify:\[\frac{ \frac{ h(3x ^{2}-3xh-1) }{ x(x+h) } }{ h }\]

Answer 5

To simplify, start by just substituting 4 in for every x. Then follow your order of operations.

Answer 6

@marihelenh quick question, how to I get rid of the bottom h? would I multiply it by the denominator in the numerator? in other words, would I multiply x(x+h) by h to get a simple fraction instead of a fraction inside of a fraction?

Answer 7

If you recall, when you divide fractions, you can multiply by the reciprocal and it will give you the same thing. So, you could multiply the top part by 1/h.