Solve (frac{sqrt{2}}{2}+1)R=2h

$$( \frac { \sqrt { 2 } } { 2 } + 1 ) R = 2 h$$

Solve for R

$$R=-2\sqrt{2}h+4h$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2\left(\frac{\sqrt{2}}{2}+1\right)R=4h$$

Use the distributive property to multiply 2 by \frac{\sqrt{2}}{2}+1.

$$\left(2\times \frac{\sqrt{2}}{2}+2\right)R=4h$$

Express 2\times \frac{\sqrt{2}}{2} as a single fraction.

$$\left(\frac{2\sqrt{2}}{2}+2\right)R=4h$$

Cancel out 2 and 2.

$$\left(\sqrt{2}+2\right)R=4h$$

Divide both sides by \sqrt{2}+2.

$$\frac{\left(\sqrt{2}+2\right)R}{\sqrt{2}+2}=\frac{4h}{\sqrt{2}+2}$$

Dividing by \sqrt{2}+2 undoes the multiplication by \sqrt{2}+2.

$$R=\frac{4h}{\sqrt{2}+2}$$

Divide 4h by \sqrt{2}+2.

$$R=-2\sqrt{2}h+4h$$

Solve for h

$$h=\frac{\sqrt{2}R}{4}+\frac{R}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2\left(\frac{\sqrt{2}}{2}+1\right)R=4h$$

Use the distributive property to multiply 2 by \frac{\sqrt{2}}{2}+1.

$$\left(2\times \frac{\sqrt{2}}{2}+2\right)R=4h$$

Express 2\times \frac{\sqrt{2}}{2} as a single fraction.

$$\left(\frac{2\sqrt{2}}{2}+2\right)R=4h$$

Cancel out 2 and 2.

$$\left(\sqrt{2}+2\right)R=4h$$

Use the distributive property to multiply \sqrt{2}+2 by R.

$$\sqrt{2}R+2R=4h$$

Swap sides so that all variable terms are on the left hand side.

$$4h=\sqrt{2}R+2R$$

Divide both sides by 4.

$$\frac{4h}{4}=\frac{\sqrt{2}R+2R}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$h=\frac{\sqrt{2}R+2R}{4}$$

Divide R\sqrt{2}+2R by 4.

$$h=\frac{\sqrt{2}R}{4}+\frac{R}{2}$$