Solve sqrt{2}(x+1)+sqrt{3}x=sqrt{2}+1

$$\sqrt { 2 } ( x + 1 ) + \sqrt { 3 } x = \sqrt { 2 } + 1$$

Solve for x

$$x=\sqrt{3}-\sqrt{2}\approx 0.317837245$$

Steps for Solving Linear Equation

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

$$\sqrt{2}x+\sqrt{2}+\sqrt{3}x=\sqrt{2}+1$$

Subtract \sqrt{2} from both sides.

$$\sqrt{2}x+\sqrt{3}x=\sqrt{2}+1-\sqrt{2}$$

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

$$\sqrt{2}x+\sqrt{3}x=1$$

Combine all terms containing x.

$$\left(\sqrt{2}+\sqrt{3}\right)x=1$$

Divide both sides by \sqrt{2}+\sqrt{3}.

$$\frac{\left(\sqrt{2}+\sqrt{3}\right)x}{\sqrt{2}+\sqrt{3}}=\frac{1}{\sqrt{2}+\sqrt{3}}$$

Dividing by \sqrt{2}+\sqrt{3} undoes the multiplication by \sqrt{2}+\sqrt{3}.

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

Divide 1 by \sqrt{2}+\sqrt{3}.

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