Question

solve for L \[d=\frac{ LR^2 }{ R^2+R^1 } \]

Answer 1

get rid of thedenominator by multiplying both sides
d(R^2+R^1)=LR^2
Divide by R^2
d(R^2+R1)/R^2=L

Answer 2

\[d = \frac{LR^2}{R^2 + R}\]
Cross multiply
\[d(R^2 + R) = LR^2\]
Divide both sides by \(R^2\) to get rid of the \(R^2\) on the right hand side, to get the value of \(L\).
\[\frac{d(R^2+R)}{R^2} = L\]
\[L = d(1 + \frac{1}{R})\]

Understood this? :)

Answer 3

Is that \(R^1\) or \(R_1\) ?
Manipulate accordingly. The steps are the same. :)

Answer 4

the second one

Answer 5

so whats next?

Answer 6

Is it \(R^2\) or \(R_2\) ?

Answer 7

I am guessing it is the subscript.

So, \(R_2, R_1, d, L\) are completely different terms. So, we have to solve for:

\[d = \frac{LR_2}{R_2 + R_1}\]

Now, to find 'L' how can we isolate it and represent it in terms of the other variables?

Step 1: Well, we can cross multiple right? [Same as multiplying \(R_2 + R_1\)on both sides]

\[d(R_2 + R_1) = \frac{LR_2}{(R_2 + R_1)} (R_2 + R_1)\]
\[d(R_2 + R_1) = \frac{LR_2}{\cancel{(R_2 + R_1)}} \cancel{(R_2 + R_1)}\]
\[d(R_2 + R_1) = LR_2\]

Step 2: I see L there, but it is multiplied to \(R_2\) [Bahh!! -_-] How can I get rid of the \(R_2\) ? Well, for one, dividing has the opposite effect of multiplying! Let's try that!

\[d \frac{(R_2 + R_1)}{R_2} = L\]

Step 3: Not necessary, but can be used to make it look more mathematical :-)

\[L = d (1 + \frac{R_1}{R_2}) \]

Getting this? :)