Solve 1/x-2=sqrt[3]{5}

$$\frac { 1 } { x - 2 } = \sqrt[ 3 ] { 5 }$$

Solve for x

$$x = \frac{5 ^ {\frac{2}{3}} + 10}{5} \approx 2.584803548$$

Steps for Solving Linear Equation

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by x-2.

$$1=\left(x-2\right)\sqrt[3]{5}$$

Use the distributive property to multiply x-2 by \sqrt[3]{5}.

$$1=x\sqrt[3]{5}-2\sqrt[3]{5}$$

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

$$x\sqrt[3]{5}-2\sqrt[3]{5}=1$$

Add 2\sqrt[3]{5} to both sides.

$$x\sqrt[3]{5}=1+2\sqrt[3]{5}$$

The equation is in standard form.

$$\sqrt[3]{5}x=2\sqrt[3]{5}+1$$

Divide both sides by \sqrt[3]{5}.

$$\frac{\sqrt[3]{5}x}{\sqrt[3]{5}}=\frac{2\sqrt[3]{5}+1}{\sqrt[3]{5}}$$

Dividing by \sqrt[3]{5} undoes the multiplication by \sqrt[3]{5}.

$$x=\frac{2\sqrt[3]{5}+1}{\sqrt[3]{5}}$$

Divide 1+2\sqrt[3]{5} by \sqrt[3]{5}.

$$x=\frac{1}{\sqrt[3]{5}}+2$$