Integration algabriac manipulation problem

[Bried]

Hello there,

I was wondering if someone might be able to help me out with some intermediate steps please. I can't see how
$$f_{tt} =-\int_{r_0}^0 \left(\frac{2Gm_0}{r} - \frac{2Gm_0}{r_0}\right)^{-\frac{1}{2}} dr$$
becomes
$$f_{tt} =- \left(\frac{2Gm_0}{r_0}\right)^{-\frac{1}{2}}\int_{r_0}^0\left(\frac{r_0}{r}-1\right)^{-\frac{1}{2}}dr$$
I've been wracking my brain over this and can't see how it's been done. I originally thought that the fraction containing all the constants was pulled out somehow but this can't be possible since
$$(A+B)^n \neq A^n + B^n$$
I would be very grateful if someone could point me in the right direction.

Regards

Brian

 

[JorisL]

You are correct with $\left( A + B \right)^n \neq A^n +B^n$.
That's not what we are using here.

We use that $\left( C\cdot A + C \cdot B\right)^n = \left[ C\left(A+b\right)\right]^n = C^n\left(A+B\right)^n$

 

[Bried]

Excellent! Thank you so much. I've just had a scribble around and got it sussed now.

Regards

Brian