Rearrange the formula

Dodi1991

Hey there, I'm having lots of difficulty with this question, I can usually do these easily, but this one really got me. The teacher gave us the answers but didn't tell us how it was worked out. If someone can go through it step by step, then I would be really grateful.

Question: Make 'u' the subject.

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

All help is appreciated.

Reply 1

DeanK2

The old cartesian sign convention...

(1/u) = (1/v) - (1/f) = (f-v)/fv [ a/b - c/d = (ad - cb)/db]

u = fv/(f - v)

multiply by vuf

OP

hmm, I don't understand this bit:

(1/v) - (1/f) = (f-v)/fv

and how come you flipped it upside down for your final answer?

and may I ask you what this means? [ a/b - c/d = (ad - cb)/db]

Sorry for my excessive amount of questions.

Reply 4

speculator

1

It's just a generic way to show how you make a common denominator.

Reply 5

The Muon

2

First of all get the u on one side and all the f and the v on the other side:

Spoiler

Then you can combine the two on the right with a common denominator.

Spoiler

Then you can simply invert both fractions

Spoiler

I have left the last steps for you to do because they are very simple.

Reply 6

Chaoslord

16

Dodi1991

hmm, I don't understand this bit:

(1/v) - (1/f) = (f-v)/fv

and how come you flipped it upside down for your final answer?

and may I ask you what this means? [ a/b - c/d = (ad - cb)/db]

Sorry for my excessive amount of questions.

\frac{a}{b} - \frac{c}{d}

multiply the left by d/d and the right by b/b (both = 1)

\frac{ad}{bd} - \frac{cb}{db}

since they have the same denominator

\frac{ad - cb}{bd}

Reply 7

Samantha-91

TRY MULTIPLYING EVERYTHING BY VUF

surely that helps... come onnnn dooooo it

Reply 8

speculator

1

I used to love doing these.....ahh good old school days!

Reply 9

Dodi1991

OP

ahhhhh, now I understand. Thank you all for helping me out. Thanks DeanK2 for the help, couldn't understand something you had but The Muon clarified it, again, thanks for the help.

Also, the way you set out out allowed me to understand very easily The Muon, thanks :>

All help was appreciated guys, thank you.

Reply 10

Samantha-91

Dodi1991

ahhhhh, now I understand. Thank you all for helping me out. Thanks DeanK2 for the help, couldn't understand something you had but The Muon clarified it, again, thanks for the help.

Also, the way you set out out allowed me to understand very easily The Muon, thanks :>

All help was appreciated guys, thank you.

Did you not do the multiplying by vuf thing???!?!?!?!

it's basically the same method...

Reply 11

Dodi1991

OP

I wasn't sure about it, and by multiplying by vuf, you mean multiply everything by vuf?

Reply 12

Samantha-91

Dodi1991

I wasn't sure about it, and by multiplying by vuf, you mean multiply everything by vuf?

Yes. Then you could've cancelled the v's in the first bit, the u's in the second bit and the f's in the 3rd bit. And voilaaaa your fractions have goneeeee

Rearrange the formula

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