Solve 3xy/2x=3y/2*x/x=3y/2

$$\frac { 3 x y } { 2 x } = \frac { 3 y } { 2 } \cdot \frac { x } { x } = \frac { 3 y } { 2 }$$

Evaluate (complex solution)

Solution Steps

Divide x by x to get 1.

$$\frac{3xy}{2x}=\frac{3y}{2}\times 1\text{ and }\frac{3y}{2}\times \frac{x}{x}=\frac{3y}{2}$$

Divide x by x to get 1.

$$\frac{3xy}{2x}=\frac{3y}{2}\times 1\text{ and }\frac{3y}{2}\times 1=\frac{3y}{2}$$

Cancel out x in both numerator and denominator.

$$\frac{3y}{2}=\frac{3y}{2}\times 1\text{ and }\frac{3y}{2}\times 1=\frac{3y}{2}$$

Express \frac{3y}{2}\times 1 as a single fraction.

$$\frac{3y}{2}=\frac{3y}{2}\text{ and }\frac{3y}{2}\times 1=\frac{3y}{2}$$

Express \frac{3y}{2}\times 1 as a single fraction.

$$\frac{3y}{2}=\frac{3y}{2}\text{ and }\frac{3y}{2}=\frac{3y}{2}$$

Subtract \frac{3y}{2} from both sides.

$$\frac{3y}{2}-\frac{3y}{2}=0\text{ and }\frac{3y}{2}=\frac{3y}{2}$$

Combine \frac{3y}{2} and -\frac{3y}{2} to get 0.

$$0=0\text{ and }\frac{3y}{2}=\frac{3y}{2}$$

Compare 0 and 0.

$$\text{true}\text{ and }\frac{3y}{2}=\frac{3y}{2}$$

Subtract \frac{3y}{2} from both sides.

$$\text{true}\text{ and }\frac{3y}{2}-\frac{3y}{2}=0$$

Combine \frac{3y}{2} and -\frac{3y}{2} to get 0.

$$\text{true}\text{ and }0=0$$

Compare 0 and 0.

$$\text{true}\text{ and }\text{true}$$

The conjunction of \text{true} and \text{true} is \text{true}.

$$\text{true}$$

Solve for x

$$x\neq 0$$

Solve for y

$$y\in \mathrm{R}$$

$$x\neq 0$$