[x^5(-3)(x^2+1)^-4(2x)]-(x^2+1)^-3(5)x^4] / (x^5)^2

Can someone show my how to simplify this, step by step? So far I got that the denominator should be x^10 because of the exponents, and (x^2+1)^-4 could be simplified as [(x+1)(x-1)]/4, likewise with (x^2+1)^-3, except the denominator is 3. Help please! Thanks much!

3 answers

The way you wrote your expression is very confusing,
e.g. in [x^5(-3)(x^2+1)^-4(2x)]
is that [x^(-15) * (x^2+1)^(-8x)] ?
or [-3x^5 * 2x/(x^2+1)^4] ?

You said (x^2+1)^-4 could be simplified as [(x+1)(x-1)]/4

this is false, x^2 + 1 does NOT factor to ((x+1)(x-1)

PLease use some more brackets, or some other way, to properly state your expression.
sorry about that. it was written like that in the book o.o''

It should be this (I think):
[x^5*(-3)*[(x^2+1)^-4]*(2x)]
- {[(x^2+1)^-3] * [(5)x^4]}
over (x^5)^2
[x^5*(-3)*[(x^2+1)^-4]*(2x)]-{[(x^2+1)^-3]*[(5)x^4]} / [ (x^5)^2 ] =
{(-3)*(2x)*(x^5)*[(x^2+1)^-4]}-{(5)+(x^4)*[((x^2)+1)^-3] / (x^7) =
(-6)*(x^6)*[((x^2)+1)^-4]-{(5)*(x^4)*[(x^2+1)^-3] / (x^7) =
{[(-6)*(x^6)*[((x^2)+1)^-4]]/x^7}-[{(5)*(x^4)*[(x^2+1)^-3] /(x^7)] =

{[(-6)*[((x^2)+1)^-4]]/x}-[(5)*[(x^2+1)^-3] /(x^3)] =

(6/(x)[((x^2)+1)^4})] - (5/(x^3)[((X^2)+1)^3]
i think