Solve x*y/2left(x+1right)+3left(x+2right)/2left(x+1right)-3=0

$$\frac{ x \times y }{ 2 \left( x+1 \right) } + \frac{ 3 \left( x+2 \right) }{ 2 \left( x+1 \right) } -3 = 0$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=3\text{, }&x\neq -1\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(x+1\right).

$$xy+3\left(x+2\right)+2\left(x+1\right)\left(-3\right)=0$$

Use the distributive property to multiply 3 by x+2.

$$xy+3x+6+2\left(x+1\right)\left(-3\right)=0$$

Multiply 2 and -3 to get -6.

$$xy+3x+6-6\left(x+1\right)=0$$

Use the distributive property to multiply -6 by x+1.

$$xy+3x+6-6x-6=0$$

Combine 3x and -6x to get -3x.

$$xy-3x+6-6=0$$

Subtract 6 from 6 to get 0.

$$xy-3x=0$$

Add 3x to both sides. Anything plus zero gives itself.

$$xy=3x$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{3x}{x}$$

Dividing by x undoes the multiplication by x.

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

Divide 3x by x.

$$y=3$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\neq -1\text{, }&y=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable x cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by 2\left(x+1\right).

$$xy+3\left(x+2\right)+2\left(x+1\right)\left(-3\right)=0$$

Use the distributive property to multiply 3 by x+2.

$$xy+3x+6+2\left(x+1\right)\left(-3\right)=0$$

Multiply 2 and -3 to get -6.

$$xy+3x+6-6\left(x+1\right)=0$$

Use the distributive property to multiply -6 by x+1.

$$xy+3x+6-6x-6=0$$

Combine 3x and -6x to get -3x.

$$xy-3x+6-6=0$$

Subtract 6 from 6 to get 0.

$$xy-3x=0$$

Combine all terms containing x.

$$\left(y-3\right)x=0$$

Divide 0 by -3+y.

$$x=0$$

Solve for y

$$\left\{\begin{matrix}y=3\text{, }&x\neq -1\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(x+1\right).

$$xy+3\left(x+2\right)+2\left(x+1\right)\left(-3\right)=0$$

Use the distributive property to multiply 3 by x+2.

$$xy+3x+6+2\left(x+1\right)\left(-3\right)=0$$

Multiply 2 and -3 to get -6.

$$xy+3x+6-6\left(x+1\right)=0$$

Use the distributive property to multiply -6 by x+1.

$$xy+3x+6-6x-6=0$$

Combine 3x and -6x to get -3x.

$$xy-3x+6-6=0$$

Subtract 6 from 6 to get 0.

$$xy-3x=0$$

Add 3x to both sides. Anything plus zero gives itself.

$$xy=3x$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{3x}{x}$$

Dividing by x undoes the multiplication by x.

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

Divide 3x by x.

$$y=3$$