Solve sqrt{3}+sqrt{12}=x+5/sqrt{3}

$$\sqrt{ 3 } + \sqrt{ 12 } = \frac{ x+5 }{ \sqrt{ 3 } }$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

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}.

$$\sqrt{3}+2\sqrt{3}=\frac{x+5}{\sqrt{3}}$$

Combine \sqrt{3} and 2\sqrt{3} to get 3\sqrt{3}.

$$3\sqrt{3}=\frac{x+5}{\sqrt{3}}$$

Rationalize the denominator of \frac{x+5}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$3\sqrt{3}=\frac{\left(x+5\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$3\sqrt{3}=\frac{\left(x+5\right)\sqrt{3}}{3}$$

Use the distributive property to multiply x+5 by \sqrt{3}.

$$3\sqrt{3}=\frac{x\sqrt{3}+5\sqrt{3}}{3}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{x\sqrt{3}+5\sqrt{3}}{3}=3\sqrt{3}$$

Multiply both sides of the equation by 3.

$$x\sqrt{3}+5\sqrt{3}=9\sqrt{3}$$

Subtract 5\sqrt{3} from both sides.

$$x\sqrt{3}=9\sqrt{3}-5\sqrt{3}$$

Combine 9\sqrt{3} and -5\sqrt{3} to get 4\sqrt{3}.

$$x\sqrt{3}=4\sqrt{3}$$

The equation is in standard form.

$$\sqrt{3}x=4\sqrt{3}$$

Divide both sides by \sqrt{3}.

$$\frac{\sqrt{3}x}{\sqrt{3}}=\frac{4\sqrt{3}}{\sqrt{3}}$$

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

$$x=\frac{4\sqrt{3}}{\sqrt{3}}$$

Divide 4\sqrt{3} by \sqrt{3}.

$$x=4$$