Identity Tables: (1-A/A0)/(1-A/A0M) => ((A0-A)/A0)/((A0M-A)/

[JRH]

I'm not too sure on how the problems should be laid out, but here goes.

I am trying to solve for M, but I can only get so far. I'm sure I saw this type of thing once in a math texbook under identity tables, it was laid out with the unsolvable equation and a simplified or reduced equivalent beside it. Anyway, I can't solve for M:

(1-A/A[sub:yntjpj62]0[/sub:yntjpj62])/(1-A/A[sub:yntjpj62]0[/sub:yntjpj62]M) => ((A[sub:yntjpj62]0[/sub:yntjpj62]-A)/A[sub:yntjpj62]0[/sub:yntjpj62])/((A[sub:yntjpj62]0[/sub:yntjpj62]M-A)/A[sub:yntjpj62]0[/sub:yntjpj62]M) => ((A[sub:yntjpj62]0[/sub:yntjpj62]-A)*M)/(A[sub:yntjpj62]0[/sub:yntjpj62]M-A) => (A[sub:yntjpj62]0[/sub:yntjpj62]M-AM)/(A[sub:yntjpj62]0[/sub:yntjpj62]M-A) =>?

Could someone please help?

Thanks in advance.

 

[JRH]

In case any of you think I have stopped looking for a response, please I could really use a hand on this one. If this is in the wrong place, please let me know.

 

[stapel]

I am trying to solve for M...

(1-A/A[sub:26zu4rz8]0[/sub:26zu4rz8])/(1-A/A[sub:26zu4rz8]0[/sub:26zu4rz8]M)

Since the above is not an equation, there is nothing to "solve". Sorry.

 

[soroban]

Hello, JRH!

You didn't give us an equation . . . so, I'll make up one.

\(\displaystyle \text{Solve for }M\!:\;\;\frac{1-\dfrac{A}{A_o}} {1-\dfrac{A}{A_oM}} \;=\;Q\)

\(\displaystyle \text{Multiply the fraction by }\frac{A_oM}{A_oM}\!:\)

. . \(\displaystyle \frac{A_oM\left(1-\frac{A}{A_o}\right)} {A_oM\left(1 - \frac{A}{A_oM}\right)} \;=\;Q \quad\Rightarrow\quad \frac{A_oM - AM}{A_oM - A} \;=\;Q \quad\Rightarrow\quad A_oM - AM \;=\;Q(A_oM - A)\)


. . \(\displaystyle A_oM - AM \;=\;A_oMQ - AQ \quad\Rightarrow\quad A_oMQ + AM - A_oM \;=\;AQ\)


\(\displaystyle \text{Factor: }\;M\left(A_oQ + A - A_o\right) \;=\;AQ \quad\Rightarrow\quad\boxed{ M \;=\;\frac{AQ}{A_oQ + A - A_o}}\)