Solve frac{2sqrt{2}}{3}=frac{3+sqrt{5}}{x}

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

Solve for x

$$x = \frac{3 {(\sqrt{10} + 3 \sqrt{2})}}{4} \approx 5.55368876$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3x, the least common multiple of 3,x.

$$x\times 2\sqrt{2}=3\left(3+\sqrt{5}\right)$$

Use the distributive property to multiply 3 by 3+\sqrt{5}.

$$x\times 2\sqrt{2}=9+3\sqrt{5}$$

The equation is in standard form.

$$2\sqrt{2}x=3\sqrt{5}+9$$

Divide both sides by 2\sqrt{2}.

$$\frac{2\sqrt{2}x}{2\sqrt{2}}=\frac{3\sqrt{5}+9}{2\sqrt{2}}$$

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

$$x=\frac{3\sqrt{5}+9}{2\sqrt{2}}$$

Divide 9+3\sqrt{5} by 2\sqrt{2}.

$$x=\frac{3\sqrt{2}\left(\sqrt{5}+3\right)}{4}$$