Solve xdiv2y=3div(x-4)

$$x \div 2y=3 \div (x-4)$$

Solve for y

$$y=\frac{6}{x\left(x-4\right)}$$

$$x\neq 4\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(x-4\right), the least common multiple of 2,x-4.

$$\left(x-4\right)xy=2\times 3$$

Use the distributive property to multiply x-4 by x.

$$\left(x^{2}-4x\right)y=2\times 3$$

Use the distributive property to multiply x^{2}-4x by y.

$$x^{2}y-4xy=2\times 3$$

Multiply 2 and 3 to get 6.

$$x^{2}y-4xy=6$$

Combine all terms containing y.

$$\left(x^{2}-4x\right)y=6$$

Divide both sides by x^{2}-4x.

$$\frac{\left(x^{2}-4x\right)y}{x^{2}-4x}=\frac{6}{x^{2}-4x}$$

Dividing by x^{2}-4x undoes the multiplication by x^{2}-4x.

$$y=\frac{6}{x^{2}-4x}$$

Divide 6 by x^{2}-4x.

$$y=\frac{6}{x\left(x-4\right)}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{4y^{2}+6y}}{y}+2$$

$$x=-\frac{\sqrt{4y^{2}+6y}}{y}+2\text{, }y\neq 0$$

Solve for x

$$x=\frac{\sqrt{4y^{2}+6y}}{y}+2$$

$$x=-\frac{\sqrt{4y^{2}+6y}}{y}+2\text{, }y>0\text{ or }y\leq -\frac{3}{2}$$