Solve x/sqrt{5-1}=frac{sqrt{5}-1}{2}

$$\frac { x } { \sqrt { 5 } - 1 } = \frac { \sqrt { 5 } - 1 } { 2 }$$

Solve for x

$$x=3-\sqrt{5}\approx 0.763932023$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$\left(\frac{1}{2}\times 5^{\frac{1}{2}}+\frac{1}{2}\right)x=\sqrt{5}-1$$

Use the distributive property to multiply \frac{1}{2}\times 5^{\frac{1}{2}}+\frac{1}{2} by x.

$$\frac{1}{2}\times 5^{\frac{1}{2}}x+\frac{1}{2}x=\sqrt{5}-1$$

Reorder the terms.

$$\frac{1}{2}\sqrt{5}x+\frac{1}{2}x=\sqrt{5}-1$$

Combine all terms containing x.

$$\left(\frac{1}{2}\sqrt{5}+\frac{1}{2}\right)x=\sqrt{5}-1$$

The equation is in standard form.

$$\frac{\sqrt{5}+1}{2}x=\sqrt{5}-1$$

Divide both sides by \frac{1}{2}\sqrt{5}+\frac{1}{2}.

$$\frac{2\times \frac{\sqrt{5}+1}{2}x}{\sqrt{5}+1}=\frac{2\left(\sqrt{5}-1\right)}{\sqrt{5}+1}$$

Dividing by \frac{1}{2}\sqrt{5}+\frac{1}{2} undoes the multiplication by \frac{1}{2}\sqrt{5}+\frac{1}{2}.

$$x=\frac{2\left(\sqrt{5}-1\right)}{\sqrt{5}+1}$$

Divide \sqrt{5}-1 by \frac{1}{2}\sqrt{5}+\frac{1}{2}.

$$x=3-\sqrt{5}$$