Simplify Equation: How to Solve for C?

[Skullmonkee]

i'm having trouble simplifying an equation.
Basically it's in the form of $$1/A=B(1/C-1/D)$$
Now what i can't to do is solve for C.

I get to $$1 = C(1/AB + 1/D)$$ but do not know where to go from there.

Any help would be much appreciated, thanks.

 

[Integral]

First of all we need to verify your starting equation, is it:

$$\frac 1 A = B (\frac 1 C - \frac 1 D )$$

 

[Mentallic]

I get to $$1 = C(1/AB + 1/D)$$ but do not know where to go from there.

Yes you're nearly there.

Let $$\frac{1}{AB}+\frac{1}{D}=x$$ so now we have $$1=Cx$$

What would you do at this point to solve (isolate the variable) for C?

 

[Skullmonkee]

Yes intergral, that is the starting equation.

Thanks Mentallic but i have a question.

If i isolate the variable, C won't i get something like this:

Let x be as you have stated. C = 1/x

Now wouldn't the equation be C = 1/(1/AB + 1/D). Is this as far as i can go?

 

[Mentallic]

Ok good, you've solved for C. However, it can be simplified further.

Are you aware of the results:

$$\frac{a}{b}+\frac{x}{y}=\frac{ay+bx}{by}$$ by finding the lowest common denominator?

and

$$\frac{1}{\left(\frac{a}{b}\right)}=\frac{b}{a}$$ ?

Applying these two ideas, you'll be able to simplify the answer

 

[Skullmonkee]

Thankyou.

I used the equations that you gave me (forgotten high school maths) and was able to get:

C = ABD/D+AB

I hope this is correct?

 

[DorianG]

That's correct all right!