Solve xsqrt{2}-sqrt{8}=xsqrt{3}-sqrt{12}

$$x \sqrt { 2 } - \sqrt { 8 } = x \sqrt { 3 } - \sqrt { 12 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$x\sqrt{2}-2\sqrt{2}=x\sqrt{3}-\sqrt{12}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

Subtract x\sqrt{3} from both sides.

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

Add 2\sqrt{2} to both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

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

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

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

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

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

$$x=2$$