Solve x+2/y+(0-x-2/2)+y/2=-1/4

$$\frac{ x+2 }{ y } +(0- \frac{ x-2 }{ 2 } )+ \frac{ y }{ 2 } = - \frac{ 1 }{ 4 }$$

Solve for x

$$x=-\frac{2y^{2}+5y+8}{2\left(2-y\right)}$$

$$y\neq 2\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4y, the least common multiple of y,2,4.

$$4\left(x+2\right)+0-2y\left(x-2\right)+2yy=-y$$

Use the distributive property to multiply 4 by x+2.

$$4x+8+0-2y\left(x-2\right)+2yy=-y$$

Add 8 and 0 to get 8.

$$4x+8-2y\left(x-2\right)+2yy=-y$$

Use the distributive property to multiply 2y by x-2.

$$4x+8-\left(2yx-4y\right)+2yy=-y$$

To find the opposite of 2yx-4y, find the opposite of each term.

$$4x+8-2yx+4y+2yy=-y$$

Multiply y and y to get y^{2}.

$$4x+8-2yx+4y+2y^{2}=-y$$

Subtract 8 from both sides.

$$4x-2yx+4y+2y^{2}=-y-8$$

Subtract 4y from both sides.

$$4x-2yx+2y^{2}=-y-8-4y$$

Combine -y and -4y to get -5y.

$$4x-2yx+2y^{2}=-5y-8$$

Subtract 2y^{2} from both sides.

$$4x-2yx=-5y-8-2y^{2}$$

Combine all terms containing x.

$$\left(4-2y\right)x=-5y-8-2y^{2}$$

The equation is in standard form.

$$\left(4-2y\right)x=-2y^{2}-5y-8$$

Divide both sides by -2y+4.

$$\frac{\left(4-2y\right)x}{4-2y}=\frac{-2y^{2}-5y-8}{4-2y}$$

Dividing by -2y+4 undoes the multiplication by -2y+4.

$$x=\frac{-2y^{2}-5y-8}{4-2y}$$

Divide -5y-8-2y^{2} by -2y+4.

$$x=-\frac{2y^{2}+5y+8}{2\left(2-y\right)}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=-\frac{\sqrt{4x^{2}-52x-39}}{4}+\frac{x}{2}-\frac{5}{4}\text{, }&\text{unconditionally}\\y=\frac{\sqrt{4x^{2}-52x-39}}{4}+\frac{x}{2}-\frac{5}{4}\text{, }&x\neq -2\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y=-\frac{\sqrt{4x^{2}-52x-39}}{4}+\frac{x}{2}-\frac{5}{4}\text{, }&x\geq 2\sqrt{13}+\frac{13}{2}\text{ or }x\leq \frac{13}{2}-2\sqrt{13}\\y=\frac{\sqrt{4x^{2}-52x-39}}{4}+\frac{x}{2}-\frac{5}{4}\text{, }&x\geq 2\sqrt{13}+\frac{13}{2}\text{ or }\left(x\neq -2\text{ and }x\leq \frac{13}{2}-2\sqrt{13}\right)\end{matrix}\right.$$