# Thread: Making f the subject

1. ## Making f the subject

Making f the subject of:

Sqrt(f+p)/sqrt(f−p)=D/d

my first step was to square, so I had:

(F+p)/(f-p) = ( D/d)^2

then multiply by (f-p)

F+p = (f-p)(D/d)^2

now I get stuck because if I now want to remove f from one side I have to subtract f but that will leave me without any f's, please help!

Thanks

kris

2. ## Re: Making f the subject

My apologise also for not writing in latex but I'm new and still trying to get to grips with it.

3. ## Re: Making f the subject

$f+p = (f-p)\left(\frac{D}{d}\right)^2$

$f+p = f\left(\frac{D}{d}\right)^2 - p\left(\frac{D}{d}\right)^2$

$p + p\left(\frac{D}{d}\right)^2 = f\left(\frac{D}{d}\right)^2 - f$

$p\left[1 + \left(\frac{D}{d}\right)^2\right] = f \left[\left(\frac{D}{d}\right)^2 - 1\right]$

$\frac{p\left[1 + \left(\frac{D}{d}\right)^2\right]}{\left[\left(\frac{D}{d}\right)^2 - 1\right]} = f$

4. ## Re: Making f the subject

Wow I don't understand how the (D/d)^2 gets on both sides and also how the f and -f don't cancel. Awesome job though, just wish I had your transposing skills,