Solve frac{sqrt{3}}{3}=k-20/k+40

$$\frac { \sqrt { 3 } } { 3 } = \frac { k - 20 } { k + 40 }$$

Solve for k

$$k=30\sqrt{3}+50\approx 101.961524227$$

Steps for Solving Linear Equation

Variable k cannot be equal to -40 since division by zero is not defined. Multiply both sides of the equation by 3\left(k+40\right), the least common multiple of 3,k+40.

$$\left(k+40\right)\sqrt{3}=3\left(k-20\right)$$

Use the distributive property to multiply k+40 by \sqrt{3}.

$$k\sqrt{3}+40\sqrt{3}=3\left(k-20\right)$$

Use the distributive property to multiply 3 by k-20.

$$k\sqrt{3}+40\sqrt{3}=3k-60$$

Subtract 3k from both sides.

$$k\sqrt{3}+40\sqrt{3}-3k=-60$$

Subtract 40\sqrt{3} from both sides.

$$k\sqrt{3}-3k=-60-40\sqrt{3}$$

Combine all terms containing k.

$$\left(\sqrt{3}-3\right)k=-60-40\sqrt{3}$$

The equation is in standard form.

$$\left(\sqrt{3}-3\right)k=-40\sqrt{3}-60$$

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

$$\frac{\left(\sqrt{3}-3\right)k}{\sqrt{3}-3}=\frac{-40\sqrt{3}-60}{\sqrt{3}-3}$$

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

$$k=\frac{-40\sqrt{3}-60}{\sqrt{3}-3}$$

Divide -60-40\sqrt{3} by \sqrt{3}-3.

$$k=30\sqrt{3}+50$$