Solve 22x+1/x+1-sqrt{2}=0

$$2 \frac { 2 x + 1 } { x + 1 } - \sqrt { 2 } = 0$$

Solve for x

$$x=\frac{\sqrt{2}-3}{7}\approx -0.22654092$$

Steps for Solving Linear Equation

Variable x cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by x+1.

$$2\left(2x+1\right)-\sqrt{2}\left(x+1\right)=0$$

Use the distributive property to multiply 2 by 2x+1.

$$4x+2-\sqrt{2}\left(x+1\right)=0$$

Use the distributive property to multiply -\sqrt{2} by x+1.

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

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

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

Add \sqrt{2} to both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 4-\sqrt{2}.

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

Dividing by 4-\sqrt{2} undoes the multiplication by 4-\sqrt{2}.

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

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

$$x=\frac{\sqrt{2}-3}{7}$$