help with lensmaker's equation

[kdmt]

I am stuck on this equation because my algebra skills are not fresh

what does this simplify into
((1/-r)-(1/r))

what i did was i found the lcd and i ended up with 2r but the solution in front of me says that it simplifies to -2/r

 

[galactus]

\(\displaystyle \L\\\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}\)

\(\displaystyle \L\\\frac{1}{-r}-\frac{1}{r}=\frac{r-(-r)}{-r^{2}}=\frac{2\not{r}}{-r^{\not{2}\text{1}}}=\frac{-2}{r}\)

Does that help refresh your memory?.

 

[Deleted member 4993]

Another way to look at it:

{1/-r} - {1/r} = -{1/r} - {1/r} = -{2/r}

 

[kdmt]

Yes, thank you