Solve frac{sqrt{3}}{3}=frac{frac{sqrt{2}}{2}}{sqrt{1/h-1}}

$$\frac { \sqrt { 3 } } { 3 } = \frac { \frac { \sqrt { 2 } } { 2 } } { \sqrt { \frac { 1 } { h - 1 } } }$$

Solve for h

$$h = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Steps for Solving Radical Equations

Multiply both sides of the equation by 3.

$$\sqrt{3}=3\left(h-1\right)^{\frac{1}{2}}\times \frac{\sqrt{2}}{2}$$

Express 3\times \frac{\sqrt{2}}{2} as a single fraction.

$$\sqrt{3}=\frac{3\sqrt{2}}{2}\left(h-1\right)^{\frac{1}{2}}$$

Multiply both sides of the equation by 2.

$$2\sqrt{3}=3\sqrt{2}\left(h-1\right)^{\frac{1}{2}}$$

Reorder the terms.

$$2\sqrt{3}=3\sqrt{2}\sqrt{h-1}$$

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

$$3\sqrt{2}\sqrt{h-1}=2\sqrt{3}$$

Divide both sides by 3\sqrt{2}.

$$\frac{3\sqrt{2}\sqrt{h-1}}{3\sqrt{2}}=\frac{2\sqrt{3}}{3\sqrt{2}}$$

Dividing by 3\sqrt{2} undoes the multiplication by 3\sqrt{2}.

$$\sqrt{h-1}=\frac{2\sqrt{3}}{3\sqrt{2}}$$

Divide 2\sqrt{3} by 3\sqrt{2}.

$$\sqrt{h-1}=\frac{\sqrt{6}}{3}$$

Square both sides of the equation.

$$h-1=\frac{2}{3}$$

Add 1 to both sides of the equation.

$$h-1-\left(-1\right)=\frac{2}{3}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$h=\frac{2}{3}-\left(-1\right)$$

Subtract -1 from \frac{2}{3}.

$$h=\frac{5}{3}$$