Question

[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!

Answer 1

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.

Answer 2

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

Answer 3

[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