Question

Need a step by step on how to solve this please

Answer 1

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

Answer 2

I have not done this in advance. I'm just going to write it down
and see what I can do with it:

[ 1/(x+3)² - 1/x² ] / 3


Multiply the top and bottom by (x+3)² :

[ 1 - (x+3)²/x² ] / 3 (x+3)²

Multiply the top and bottom by x² :

[ x² - (x+3)² ] / 3 x² (x+3)²

Now it's just a matter of expanding and cleaning things up,
and hope and pray that a lot of things cancel.

Eliminate the parentheses on top and bottom:

[ x² - x² - 6x -9 ] / 3 x² (x² + 6x + 9)

Combine the x² terms on top, and divide top and bottom by 3 :

[ - 2x - 3 ] / x² (x² + 6x + 9)

Finally, all I can make of this is:

- (2x + 3) / [ x(x+3) ]² .

That's not a whole lot prettier than the original form, but at least
we got rid of those fractions in the numerator of a fraction.

I hope this is some help to you.