Solve BC+10/sqrt{3}=BC

$$\frac { B C + 10 } { \sqrt { 3 } } = B C$$

Solve for B

$$B=\frac{5\left(\sqrt{3}+1\right)}{C}$$

$$C\neq 0$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{BC+10}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(BC+10\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}=BC$$

The square of \sqrt{3} is 3.

$$\frac{\left(BC+10\right)\sqrt{3}}{3}=BC$$

Use the distributive property to multiply BC+10 by \sqrt{3}.

$$\frac{BC\sqrt{3}+10\sqrt{3}}{3}=BC$$

Subtract BC from both sides.

$$\frac{BC\sqrt{3}+10\sqrt{3}}{3}-BC=0$$

Multiply both sides of the equation by 3.

$$BC\sqrt{3}+10\sqrt{3}-3BC=0$$

Reorder the terms.

$$\sqrt{3}BC-3BC+10\sqrt{3}=0$$

Subtract 10\sqrt{3} from both sides. Anything subtracted from zero gives its negation.

$$\sqrt{3}BC-3BC=-10\sqrt{3}$$

Combine all terms containing B.

$$\left(\sqrt{3}C-3C\right)B=-10\sqrt{3}$$

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

$$\frac{\left(\sqrt{3}C-3C\right)B}{\sqrt{3}C-3C}=-\frac{10\sqrt{3}}{\sqrt{3}C-3C}$$

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

$$B=-\frac{10\sqrt{3}}{\sqrt{3}C-3C}$$

Divide -10\sqrt{3} by \sqrt{3}C-3C.

$$B=\frac{5\left(\sqrt{3}+1\right)}{C}$$

Solve for C

$$C=\frac{5\left(\sqrt{3}+1\right)}{B}$$

$$B\neq 0$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{BC+10}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(BC+10\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}=BC$$

The square of \sqrt{3} is 3.

$$\frac{\left(BC+10\right)\sqrt{3}}{3}=BC$$

Use the distributive property to multiply BC+10 by \sqrt{3}.

$$\frac{BC\sqrt{3}+10\sqrt{3}}{3}=BC$$

Subtract BC from both sides.

$$\frac{BC\sqrt{3}+10\sqrt{3}}{3}-BC=0$$

Multiply both sides of the equation by 3.

$$BC\sqrt{3}+10\sqrt{3}-3BC=0$$

Reorder the terms.

$$\sqrt{3}BC-3BC+10\sqrt{3}=0$$

Subtract 10\sqrt{3} from both sides. Anything subtracted from zero gives its negation.

$$\sqrt{3}BC-3BC=-10\sqrt{3}$$

Combine all terms containing C.

$$\left(\sqrt{3}B-3B\right)C=-10\sqrt{3}$$

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

$$\frac{\left(\sqrt{3}B-3B\right)C}{\sqrt{3}B-3B}=-\frac{10\sqrt{3}}{\sqrt{3}B-3B}$$

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

$$C=-\frac{10\sqrt{3}}{\sqrt{3}B-3B}$$

Divide -10\sqrt{3} by \sqrt{3}B-3B.

$$C=\frac{5\left(\sqrt{3}+1\right)}{B}$$