Solve RT2=1/frac{1{200Omega}+1/100Omega+1/410Omega}

$$RT 2 = \frac { 1 } { \frac { 1 } { 200 \Omega } + \frac { 1 } { 100 \Omega } + \frac { 1 } { 410 \Omega } }$$

Solve for R

$$R=\frac{8200\Omega }{143T_{2}}$$

$$T_{2}\neq 0\text{ and }\Omega \neq 0$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 200\Omega and 100\Omega is 200\Omega . Multiply \frac{1}{100\Omega } times \frac{2}{2}.

$$RT_{2}=\frac{1}{\frac{1}{200\Omega }+\frac{2}{200\Omega }+\frac{1}{410\Omega }}$$

Since \frac{1}{200\Omega } and \frac{2}{200\Omega } have the same denominator, add them by adding their numerators. Add 1 and 2 to get 3.

$$RT_{2}=\frac{1}{\frac{3}{200\Omega }+\frac{1}{410\Omega }}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 200\Omega and 410\Omega is 8200\Omega . Multiply \frac{3}{200\Omega } times \frac{41}{41}. Multiply \frac{1}{410\Omega } times \frac{20}{20}.

$$RT_{2}=\frac{1}{\frac{3\times 41}{8200\Omega }+\frac{20}{8200\Omega }}$$

Since \frac{3\times 41}{8200\Omega } and \frac{20}{8200\Omega } have the same denominator, add them by adding their numerators.

$$RT_{2}=\frac{1}{\frac{3\times 41+20}{8200\Omega }}$$

Do the multiplications in 3\times 41+20.

$$RT_{2}=\frac{1}{\frac{123+20}{8200\Omega }}$$

Do the calculations in 123+20.

$$RT_{2}=\frac{1}{\frac{143}{8200\Omega }}$$

Divide 1 by \frac{143}{8200\Omega } by multiplying 1 by the reciprocal of \frac{143}{8200\Omega }.

$$RT_{2}=\frac{8200\Omega }{143}$$

Multiply both sides of the equation by 143.

$$143RT_{2}=8200\Omega$$

The equation is in standard form.

$$143T_{2}R=8200\Omega$$

Divide both sides by 143T_{2}.

$$\frac{143T_{2}R}{143T_{2}}=\frac{8200\Omega }{143T_{2}}$$

Dividing by 143T_{2} undoes the multiplication by 143T_{2}.

$$R=\frac{8200\Omega }{143T_{2}}$$

Solve for T_2

$$T_{2}=\frac{8200\Omega }{143R}$$

$$R\neq 0\text{ and }\Omega \neq 0$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 200\Omega and 100\Omega is 200\Omega . Multiply \frac{1}{100\Omega } times \frac{2}{2}.

$$RT_{2}=\frac{1}{\frac{1}{200\Omega }+\frac{2}{200\Omega }+\frac{1}{410\Omega }}$$

Since \frac{1}{200\Omega } and \frac{2}{200\Omega } have the same denominator, add them by adding their numerators. Add 1 and 2 to get 3.

$$RT_{2}=\frac{1}{\frac{3}{200\Omega }+\frac{1}{410\Omega }}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 200\Omega and 410\Omega is 8200\Omega . Multiply \frac{3}{200\Omega } times \frac{41}{41}. Multiply \frac{1}{410\Omega } times \frac{20}{20}.

$$RT_{2}=\frac{1}{\frac{3\times 41}{8200\Omega }+\frac{20}{8200\Omega }}$$

Since \frac{3\times 41}{8200\Omega } and \frac{20}{8200\Omega } have the same denominator, add them by adding their numerators.

$$RT_{2}=\frac{1}{\frac{3\times 41+20}{8200\Omega }}$$

Do the multiplications in 3\times 41+20.

$$RT_{2}=\frac{1}{\frac{123+20}{8200\Omega }}$$

Do the calculations in 123+20.

$$RT_{2}=\frac{1}{\frac{143}{8200\Omega }}$$

Divide 1 by \frac{143}{8200\Omega } by multiplying 1 by the reciprocal of \frac{143}{8200\Omega }.

$$RT_{2}=\frac{8200\Omega }{143}$$

Multiply both sides of the equation by 143.

$$143RT_{2}=8200\Omega$$

Divide both sides by 143R.

$$\frac{143RT_{2}}{143R}=\frac{8200\Omega }{143R}$$

Dividing by 143R undoes the multiplication by 143R.

$$T_{2}=\frac{8200\Omega }{143R}$$