Solve LC_{1}r+1/h-1=1/2

$$L C _ { 1 } \frac { r + 1 } { h - 1 } = \frac { 1 } { 2 }$$

Solve for C_1

$$C_{1}=-\frac{1-h}{2L\left(r+1\right)}$$

$$r\neq -1\text{ and }L\neq 0\text{ and }h\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(h-1\right), the least common multiple of h-1,2.

$$LC_{1}\times 2\left(r+1\right)=h-1$$

Use the distributive property to multiply LC_{1}\times 2 by r+1.

$$2LC_{1}r+LC_{1}\times 2=h-1$$

Combine all terms containing C_{1}.

$$\left(2Lr+L\times 2\right)C_{1}=h-1$$

The equation is in standard form.

$$\left(2Lr+2L\right)C_{1}=h-1$$

Divide both sides by 2Lr+2L.

$$\frac{\left(2Lr+2L\right)C_{1}}{2Lr+2L}=\frac{h-1}{2Lr+2L}$$

Dividing by 2Lr+2L undoes the multiplication by 2Lr+2L.

$$C_{1}=\frac{h-1}{2Lr+2L}$$

Divide h-1 by 2Lr+2L.

$$C_{1}=\frac{h-1}{2L\left(r+1\right)}$$

Solve for L

$$L=-\frac{1-h}{2C_{1}\left(r+1\right)}$$

$$r\neq -1\text{ and }C_{1}\neq 0\text{ and }h\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(h-1\right), the least common multiple of h-1,2.

$$LC_{1}\times 2\left(r+1\right)=h-1$$

Use the distributive property to multiply LC_{1}\times 2 by r+1.

$$2LC_{1}r+LC_{1}\times 2=h-1$$

Combine all terms containing L.

$$\left(2C_{1}r+C_{1}\times 2\right)L=h-1$$

The equation is in standard form.

$$\left(2C_{1}r+2C_{1}\right)L=h-1$$

Divide both sides by 2C_{1}+2C_{1}r.

$$\frac{\left(2C_{1}r+2C_{1}\right)L}{2C_{1}r+2C_{1}}=\frac{h-1}{2C_{1}r+2C_{1}}$$

Dividing by 2C_{1}+2C_{1}r undoes the multiplication by 2C_{1}+2C_{1}r.

$$L=\frac{h-1}{2C_{1}r+2C_{1}}$$

Divide h-1 by 2C_{1}+2C_{1}r.

$$L=\frac{h-1}{2C_{1}\left(r+1\right)}$$