Solve 161V=188v*frac{R_{1}}{R_{1}+21Omega}

$$161 V = 188 v \cdot \frac { R _ { 1 } } { R _ { 1 } + 21 \Omega }$$

Solve for V

$$V=\frac{188R_{1}v}{161\left(R_{1}+21\Omega \right)}$$

$$R_{1}\neq -21\Omega$$

Steps for Solving Linear Equation

Multiply both sides of the equation by R_{1}+21\Omega .

$$161V\left(R_{1}+21\Omega \right)=188vR_{1}$$

Use the distributive property to multiply 161V by R_{1}+21\Omega .

$$161VR_{1}+3381\Omega V=188vR_{1}$$

Combine all terms containing V.

$$\left(161R_{1}+3381\Omega \right)V=188vR_{1}$$

The equation is in standard form.

$$\left(161R_{1}+3381\Omega \right)V=188R_{1}v$$

Divide both sides by 161R_{1}+3381\Omega .

$$\frac{\left(161R_{1}+3381\Omega \right)V}{161R_{1}+3381\Omega }=\frac{188R_{1}v}{161R_{1}+3381\Omega }$$

Dividing by 161R_{1}+3381\Omega undoes the multiplication by 161R_{1}+3381\Omega .

$$V=\frac{188R_{1}v}{161R_{1}+3381\Omega }$$

Divide 188vR_{1} by 161R_{1}+3381\Omega .

$$V=\frac{188R_{1}v}{161\left(R_{1}+21\Omega \right)}$$

Solve for R_1

$$\left\{\begin{matrix}R_{1}=\frac{3381V\Omega }{188v-161V}\text{, }&\Omega \neq 0\text{ and }v\neq 0\text{ and }V\neq \frac{188v}{161}\\R_{1}\neq 0\text{, }&\Omega =0\text{ and }v=\frac{161V}{188}\text{ and }V\neq 0\\R_{1}\neq -21\Omega \text{, }&V=0\text{ and }v=0\end{matrix}\right.$$