Solve p_{p}=1/R-j1/omega*L

$$p _ { p } = \frac { 1 } { R } - j \frac { 1 } { \omega * L }$$

Solve for L

$$\left\{\begin{matrix}L=-\frac{Rj}{\omega \left(Rp_{p}-1\right)}\text{, }&R\neq 0\text{ and }j\neq 0\text{ and }p_{p}\neq \frac{1}{R}\text{ and }\omega \neq 0\\L\neq 0\text{, }&R\neq 0\text{ and }p_{p}=\frac{1}{R}\text{ and }j=0\text{ and }\omega \neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable L cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by LR\omega , the least common multiple of R,\omega L.

$$p_{p}LR\omega =L\omega -jR\times 1$$

Subtract L\omega from both sides.

$$p_{p}LR\omega -L\omega =-jR$$

Combine all terms containing L.

$$\left(p_{p}R\omega -\omega \right)L=-jR$$

The equation is in standard form.

$$\left(Rp_{p}\omega -\omega \right)L=-Rj$$

Divide both sides by Rp_{p}\omega -\omega .

$$\frac{\left(Rp_{p}\omega -\omega \right)L}{Rp_{p}\omega -\omega }=-\frac{Rj}{Rp_{p}\omega -\omega }$$

Dividing by Rp_{p}\omega -\omega undoes the multiplication by Rp_{p}\omega -\omega .

$$L=-\frac{Rj}{Rp_{p}\omega -\omega }$$

Divide -jR by Rp_{p}\omega -\omega .

$$L=-\frac{Rj}{\omega \left(Rp_{p}-1\right)}$$

Variable L cannot be equal to 0.

$$L=-\frac{Rj}{\omega \left(Rp_{p}-1\right)}\text{, }L\neq 0$$

Solve for R

$$R=\frac{L\omega }{Lp_{p}\omega +j}$$

$$\omega \neq 0\text{ and }L\neq 0\text{ and }j\neq -Lp_{p}\omega \text{ and }p_{p}\neq -\frac{j}{L\omega }$$

Steps for Solving Linear Equation

Variable R cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by LR\omega , the least common multiple of R,\omega L.

$$p_{p}LR\omega =L\omega -jR\times 1$$

Add jR\times 1 to both sides.

$$p_{p}LR\omega +jR\times 1=L\omega$$

Reorder the terms.

$$LRp_{p}\omega +Rj=L\omega$$

Combine all terms containing R.

$$\left(Lp_{p}\omega +j\right)R=L\omega$$

Divide both sides by p_{p}L\omega +j.

$$\frac{\left(Lp_{p}\omega +j\right)R}{Lp_{p}\omega +j}=\frac{L\omega }{Lp_{p}\omega +j}$$

Dividing by p_{p}L\omega +j undoes the multiplication by p_{p}L\omega +j.

$$R=\frac{L\omega }{Lp_{p}\omega +j}$$

Variable R cannot be equal to 0.

$$R=\frac{L\omega }{Lp_{p}\omega +j}\text{, }R\neq 0$$