Solve frac{4sqrt{3}}{3+a}=frac{sqrt{3}}{2}

$$\frac { 4 \sqrt { 3 } } { 3 + a } = \frac { \sqrt { 3 } } { 2 }$$

Solve for a

$$a=5$$

Steps for Solving Linear Equation

Variable a cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by 2\left(a+3\right), the least common multiple of 3+a,2.

$$2\times 4\sqrt{3}=\left(a+3\right)\sqrt{3}$$

Multiply 2 and 4 to get 8.

$$8\sqrt{3}=\left(a+3\right)\sqrt{3}$$

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

$$8\sqrt{3}=a\sqrt{3}+3\sqrt{3}$$

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

$$a\sqrt{3}+3\sqrt{3}=8\sqrt{3}$$

Subtract 3\sqrt{3} from both sides.

$$a\sqrt{3}=8\sqrt{3}-3\sqrt{3}$$

Combine 8\sqrt{3} and -3\sqrt{3} to get 5\sqrt{3}.

$$a\sqrt{3}=5\sqrt{3}$$

The equation is in standard form.

$$\sqrt{3}a=5\sqrt{3}$$

Divide both sides by \sqrt{3}.

$$\frac{\sqrt{3}a}{\sqrt{3}}=\frac{5\sqrt{3}}{\sqrt{3}}$$

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

$$a=\frac{5\sqrt{3}}{\sqrt{3}}$$

Divide 5\sqrt{3} by \sqrt{3}.

$$a=5$$