I can't seem to follow the manipulation of the equation

[Kasper Larssen]

Hello!

In the picture below, i can't seem to understand how they get from the first line, to the second line.

(https://imgur.com/a/Fal3T)

When i write it up as dr/dT on the leftside, and separate the r's and the T's, i get dr/((1/2)*r-(1/16)*r^5)=dT which is not the same as in the picture.

Where do i go wrong?

 

[Orodruin]

How is it not the same thing? It is exactly the same thing just factorising out $r/2$ from the denominator.

 

[Ray Vickson]

Hello!

In the picture below, i can't seem to understand how they get from the first line, to the second line.

(https://imgur.com/a/Fal3T)

When i write it up as dr/dT on the leftside, and separate the r's and the T's, i get dr/((1/2)*r-(1/16)*r^5)=dT which is not the same as in the picture.

Where do i go wrong?

You forgot Algebra 101: just multiply your numerator and denominator by 2.