Solve frac{5sqrt{6}2}{frac{sqrt{2}}{2}}=x/sqrt{3/2}

$$\frac{ 5 \sqrt{ 6 } 2 }{ \frac{ \sqrt{ 2 } }{ 2 } } = \frac{ x }{ \frac{ \sqrt{ 3 } }{ 2 } }$$

Solve for x

$$x=30$$

Steps for Solving Linear Equation

Multiply 2 and 5 to get 10.

$$\frac{10\sqrt{6}}{\frac{\sqrt{2}}{2}}=\frac{x}{\frac{\sqrt{3}}{2}}$$

Divide 10\sqrt{6} by \frac{\sqrt{2}}{2} by multiplying 10\sqrt{6} by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{10\sqrt{6}\times 2}{\sqrt{2}}=\frac{x}{\frac{\sqrt{3}}{2}}$$

Rationalize the denominator of \frac{10\sqrt{6}\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{10\sqrt{6}\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}=\frac{x}{\frac{\sqrt{3}}{2}}$$

The square of \sqrt{2} is 2.

$$\frac{10\sqrt{6}\times 2\sqrt{2}}{2}=\frac{x}{\frac{\sqrt{3}}{2}}$$

Multiply 10 and 2 to get 20.

$$\frac{20\sqrt{6}\sqrt{2}}{2}=\frac{x}{\frac{\sqrt{3}}{2}}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$\frac{20\sqrt{2}\sqrt{3}\sqrt{2}}{2}=\frac{x}{\frac{\sqrt{3}}{2}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{20\times 2\sqrt{3}}{2}=\frac{x}{\frac{\sqrt{3}}{2}}$$

Cancel out 2 and 2.

$$20\sqrt{3}=\frac{x}{\frac{\sqrt{3}}{2}}$$

Divide x by \frac{\sqrt{3}}{2} by multiplying x by the reciprocal of \frac{\sqrt{3}}{2}.

$$20\sqrt{3}=\frac{x\times 2}{\sqrt{3}}$$

Rationalize the denominator of \frac{x\times 2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$20\sqrt{3}=\frac{x\times 2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$20\sqrt{3}=\frac{x\times 2\sqrt{3}}{3}$$

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

$$\frac{x\times 2\sqrt{3}}{3}=20\sqrt{3}$$

Multiply both sides of the equation by 3.

$$x\times 2\sqrt{3}=60\sqrt{3}$$

The equation is in standard form.

$$2\sqrt{3}x=60\sqrt{3}$$

Divide both sides by 2\sqrt{3}.

$$\frac{2\sqrt{3}x}{2\sqrt{3}}=\frac{60\sqrt{3}}{2\sqrt{3}}$$

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

$$x=\frac{60\sqrt{3}}{2\sqrt{3}}$$

Divide 60\sqrt{3} by 2\sqrt{3}.

$$x=30$$