Solve 2x/k+3=x/3k

$$\frac { 2 x } { k + 3 } = \frac { x } { 3 k }$$

Solve for k (complex solution)

$$\left\{\begin{matrix}\\k=\frac{3}{5}=0.6\text{, }&\text{unconditionally}\\k\in \mathrm{C}\setminus -3,0\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable k cannot be equal to any of the values -3,0 since division by zero is not defined. Multiply both sides of the equation by 3k\left(k+3\right), the least common multiple of k+3,3k.

$$3k\times 2x=\left(k+3\right)x$$

Multiply 3 and 2 to get 6.

$$6kx=\left(k+3\right)x$$

Use the distributive property to multiply k+3 by x.

$$6kx=kx+3x$$

Subtract kx from both sides.

$$6kx-kx=3x$$

Combine 6kx and -kx to get 5kx.

$$5kx=3x$$

The equation is in standard form.

$$5xk=3x$$

Divide both sides by 5x.

$$\frac{5xk}{5x}=\frac{3x}{5x}$$

Dividing by 5x undoes the multiplication by 5x.

$$k=\frac{3x}{5x}$$

Divide 3x by 5x.

$$k=\frac{3}{5}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=0\text{, }&k\neq -3\text{ and }k\neq 0\\x\in \mathrm{C}\text{, }&k=\frac{3}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3k\left(k+3\right), the least common multiple of k+3,3k.

$$3k\times 2x=\left(k+3\right)x$$

Multiply 3 and 2 to get 6.

$$6kx=\left(k+3\right)x$$

Use the distributive property to multiply k+3 by x.

$$6kx=kx+3x$$

Subtract kx from both sides.

$$6kx-kx=3x$$

Combine 6kx and -kx to get 5kx.

$$5kx=3x$$

Subtract 3x from both sides.

$$5kx-3x=0$$

Combine all terms containing x.

$$\left(5k-3\right)x=0$$

Divide 0 by 5k-3.

$$x=0$$

Solve for k

$$\left\{\begin{matrix}\\k=\frac{3}{5}=0.6\text{, }&\text{unconditionally}\\k\in \mathrm{R}\setminus -3,0\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable k cannot be equal to any of the values -3,0 since division by zero is not defined. Multiply both sides of the equation by 3k\left(k+3\right), the least common multiple of k+3,3k.

$$3k\times 2x=\left(k+3\right)x$$

Multiply 3 and 2 to get 6.

$$6kx=\left(k+3\right)x$$

Use the distributive property to multiply k+3 by x.

$$6kx=kx+3x$$

Subtract kx from both sides.

$$6kx-kx=3x$$

Combine 6kx and -kx to get 5kx.

$$5kx=3x$$

The equation is in standard form.

$$5xk=3x$$

Divide both sides by 5x.

$$\frac{5xk}{5x}=\frac{3x}{5x}$$

Dividing by 5x undoes the multiplication by 5x.

$$k=\frac{3x}{5x}$$

Divide 3x by 5x.

$$k=\frac{3}{5}$$

Solve for x

$$\left\{\begin{matrix}x=0\text{, }&k\neq -3\text{ and }k\neq 0\\x\in \mathrm{R}\text{, }&k=\frac{3}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3k\left(k+3\right), the least common multiple of k+3,3k.

$$3k\times 2x=\left(k+3\right)x$$

Multiply 3 and 2 to get 6.

$$6kx=\left(k+3\right)x$$

Use the distributive property to multiply k+3 by x.

$$6kx=kx+3x$$

Subtract kx from both sides.

$$6kx-kx=3x$$

Combine 6kx and -kx to get 5kx.

$$5kx=3x$$

Subtract 3x from both sides.

$$5kx-3x=0$$

Combine all terms containing x.

$$\left(5k-3\right)x=0$$

Divide 0 by 5k-3.

$$x=0$$