rtnl exponents: x^2[(1/2)(9-x^(-1/2)(-2x)]+(9-x^2)^(1/2)(2x)

[bluewhale210]

i think this one is confusing me just because of all the () the problem is

x^2[(1/2)(9-x^(-1/2)(-2x)]+(9-x^2)^(1/2)(2x) sence this porblem had all these () i

called (9-x^2) W and then i called 2x K

to get x^2[(1/2)W^(-1/2)-K}+W^(1/2)K

i try to take out W^(-1/2) and K

but it cames out to be [x^2(1/2)k+W]/W^1/2

and i dont think it is right can u show me my mistake or if i miss a step

if u have any thought on how to help please do!!!!!!

 

[Unco]

Re: it another factoring with rational exponents

i think this one is confusing me just because of all the () the problem is

x^2[(1/2)(9-x^2)^(-1/2)(-2x)]+(9-x^2)^(1/2)(2x) sence this porblem had all these () i

called (9-x^2) W and then i called 2x K

to get x^2[(1/2)W^(-1/2)(-K)}+W^(1/2)K (*)

i try to take out W^(-1/2) and K

but it cames out to be [x^2(1/2)k+W]/W^1/2
If you factor out W^(-1/2) and K from (*) you should get
KW^(-1/2)[-(1/2)x^2 + W], from which you can resubstitute and simplify.

and i dont think it is right can u show me my mistake or if i miss a step

if u have any thought on how to help please do!!!!!!

 

[Denis]

x^2[(1/2) (9 - x^2)^(-1/2) (-2x)] + (9 - x^2)^(1/2) (2x)

Another way:

1st term has 1/2 times -2x, which equals -x; rewrite:

x^2[-x (9 - x^2)^(-1/2)] + 2x (9 - x^2)^(1/2)

Let W = 9 - x^2; then we have:

x^2[-x W^(-1/2)] + 2x W^(1/2)

= x^2[-x / W^(1/2)] + 2x W^(1/2)

= -x^3 / W^(1/2) + 2x W^(1/2)

= (-x^3 + 2x W) / W^(1/2)

= x( 2W - x^2) / W^(1/2) ; re-substitute for W:

= x[2(9 - x^2) - x^2] / (9 - x^2)^(1/2)

= x(18 - 2x^2 - x^2) / (9 - x^2)^(1/2)

= x(18 - 3x^2) / (9 - x^2)^(1/2)

= 3x(6 - x^2) / (9 - x^2)^(1/2)

Phewwwww..... :shock: