Solve 4x^2/xsqrt{2}=4x/sqrt{2}=2xsqrt{2}

$$\frac{ 4 { x }^{ 2 } }{ x \sqrt{ 2 } } = \frac{ 4x }{ \sqrt{ 2 } } =2x \sqrt{ 2 }$$

Evaluate (complex solution)

Solution Steps

Remove the parentheses around x.

$$\frac{4x^{2}}{x\sqrt{2}}=\frac{4x}{\sqrt{2}}\text{ and }\frac{4x}{\sqrt{2}}=2x\sqrt{2}$$

Cancel out x in both numerator and denominator.

$$\frac{4x}{\sqrt{2}}=\frac{4x}{\sqrt{2}}\text{ and }\frac{4x}{\sqrt{2}}=2x\sqrt{2}$$

Rationalize the denominator of \frac{4x}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{4x\sqrt{2}}{\left(\sqrt{2}\right)^{2}}=\frac{4x}{\sqrt{2}}\text{ and }\frac{4x}{\sqrt{2}}=2x\sqrt{2}$$

The square of \sqrt{2} is 2.

$$\frac{4x\sqrt{2}}{2}=\frac{4x}{\sqrt{2}}\text{ and }\frac{4x}{\sqrt{2}}=2x\sqrt{2}$$

Rationalize the denominator of \frac{4x}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{4x\sqrt{2}}{2}=\frac{4x\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\text{ and }\frac{4x}{\sqrt{2}}=2x\sqrt{2}$$

The square of \sqrt{2} is 2.

$$\frac{4x\sqrt{2}}{2}=\frac{4x\sqrt{2}}{2}\text{ and }\frac{4x}{\sqrt{2}}=2x\sqrt{2}$$

Rationalize the denominator of \frac{4x}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{4x\sqrt{2}}{2}=\frac{4x\sqrt{2}}{2}\text{ and }\frac{4x\sqrt{2}}{\left(\sqrt{2}\right)^{2}}=2x\sqrt{2}$$

The square of \sqrt{2} is 2.

$$\frac{4x\sqrt{2}}{2}=\frac{4x\sqrt{2}}{2}\text{ and }\frac{4x\sqrt{2}}{2}=2x\sqrt{2}$$

Divide 4x\sqrt{2} by 2 to get 2x\sqrt{2}.

$$2x\sqrt{2}=\frac{4x\sqrt{2}}{2}\text{ and }\frac{4x\sqrt{2}}{2}=2x\sqrt{2}$$

Divide 4x\sqrt{2} by 2 to get 2x\sqrt{2}.

$$2x\sqrt{2}=2x\sqrt{2}\text{ and }\frac{4x\sqrt{2}}{2}=2x\sqrt{2}$$

Subtract 2x\sqrt{2} from both sides.

$$2x\sqrt{2}-2x\sqrt{2}=0\text{ and }\frac{4x\sqrt{2}}{2}=2x\sqrt{2}$$

Combine 2x\sqrt{2} and -2x\sqrt{2} to get 0.

$$0=0\text{ and }\frac{4x\sqrt{2}}{2}=2x\sqrt{2}$$

Compare 0 and 0.

$$\text{true}\text{ and }\frac{4x\sqrt{2}}{2}=2x\sqrt{2}$$

Divide 4x\sqrt{2} by 2 to get 2x\sqrt{2}.

$$\text{true}\text{ and }2x\sqrt{2}=2x\sqrt{2}$$

Subtract 2x\sqrt{2} from both sides.

$$\text{true}\text{ and }2x\sqrt{2}-2x\sqrt{2}=0$$

Combine 2x\sqrt{2} and -2x\sqrt{2} to get 0.

$$\text{true}\text{ and }0=0$$

Compare 0 and 0.

$$\text{true}\text{ and }\text{true}$$

The conjunction of \text{true} and \text{true} is \text{true}.

$$\text{true}$$

Solve for x

$$x\neq 0$$