Solve x+4/x=sqrt{2}

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

Solve for x

$$x=4\left(\sqrt{2}+1\right)\approx 9.656854249$$

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 x.

$$x+4=x\sqrt{2}$$

Subtract x\sqrt{2} from both sides.

$$x+4-x\sqrt{2}=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$x-x\sqrt{2}=-4$$

Combine all terms containing x.

$$\left(1-\sqrt{2}\right)x=-4$$

Divide both sides by 1-\sqrt{2}.

$$\frac{\left(1-\sqrt{2}\right)x}{1-\sqrt{2}}=-\frac{4}{1-\sqrt{2}}$$

Dividing by 1-\sqrt{2} undoes the multiplication by 1-\sqrt{2}.

$$x=-\frac{4}{1-\sqrt{2}}$$

Divide -4 by 1-\sqrt{2}.

$$x=4\sqrt{2}+4$$