Thin lens equation for diverging lenses.

[nblu]

Hi, I was reading a section which explains about the
"thin lens equation for diverging lenses" and it included an example;

Formula:
1/f = 1/di + 1/do
where f is the focal distance,
di is the distance of the image from the center and,
do is the distance of the object from the center.

Example:
f = -4cm
do = 3cm
di = ?

1/di = 1/f - 1/do
1/di = -1/4cm - 1/3cm
1/di = -3/12cm - 4/12cm
1/di = -7/12cm
1/di = -12/7cm = -1.7cm

The part where I have a confusion is colored in red.
I've been questioning, why -7/12cm was flipped in the last step.

If that example was to be solved as decimal numbers it would be;
1/di = -0.250cm^-1 - 0.333cm^-1
1/di = -1/0.583cm
then in this case, I would understand why the number has been reversed because it was ^-1
but when solving in fraction, I get confused..

Could anybody please explain for me?
Thank you in advance

 

[Doc Al]

1/di = 1/f - 1/do
1/di = -1/4cm - 1/3cm
1/di = -3/12cm - 4/12cm
1/di = -7/12cm
1/di = -12/7cm = -1.7cm

The part where I have a confusion is colored in red.
I've been questioning, why -7/12cm was flipped in the last step.

I assume it's a typo. That last line should have read:
di = -12/7cm = -1.7cm

I assume that you understand that: 1/x = a/b can be inverted (as long as you're not dividing by zero) to become x = b/a.