Question

Simplify.

Answer 1

what

Answer 2

\[\frac{\left[ 1/(x+h)^{2} \right]-\left[ 1/x ^{2} \right] }{ h }\]

Answer 3

bunch of algebra
it is best to forget about the \(h\) in the denominator until last, and concentrate on
\[\frac{1}{(x+h)^2}-\frac{1}{x^2}\]

Answer 4

then subtract the way you always subtract fractions :\[\frac{1}{(x+h)^2}-\frac{1}{x^2}=\frac{x^2-(x+h)^2}{x^2(x+h)^2}\]

Answer 5

leave the denominator in factored form

Answer 6

expand the numerator (carefully) and combine like terms. use parentheses
\[\frac{x^2-[x^2+2xh+h^2]}{x^2(x+h)^2}\]

Answer 7

you good from there?

Answer 8

Yeah, mostly. Do I still leave the \[h\] out or are there more steps?

Answer 9

when you get done messing around in the numerator you will only have two terms, both with an \(h\)
factor it out then cancel with the \(h\) in the denominator that we have been ignoring

Answer 10

ah....?

Answer 11

\[\frac{x^2-[x^2+2xh+h^2]}{x^2(x+h)^2}=\frac{-2xh-h^2}{x^2(x+h)^2}\]\[=\frac{h(-x-h)}{x^2(x+h)^2}\]

Answer 12

now recall that \(h\) in the denominator that we ignored so this really should be \[=\frac{h(-x-h)}{x^2(x+h)^2h}\]

Answer 13

So that's the final answer?

Answer 14

Okay, so I'll come back to this problem as a structure guide for the next few. Thanks bunches :)