Solve x^2+6/2+2=9+2/y

$$\frac { x ^ { 2 } + 6 } { 2 + 2 } = \frac { 9 + 2 } { y }$$

Solve for y (complex solution)

$$y=\frac{44}{x^{2}+6}$$

$$x\neq -\sqrt{6}i\text{ and }x\neq \sqrt{6}i$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.

$$\frac{1}{4}y\left(x^{2}+6\right)=9+2$$

Use the distributive property to multiply \frac{1}{4}y by x^{2}+6.

$$\frac{1}{4}yx^{2}+\frac{3}{2}y=9+2$$

Add 9 and 2 to get 11.

$$\frac{1}{4}yx^{2}+\frac{3}{2}y=11$$

Combine all terms containing y.

$$\left(\frac{1}{4}x^{2}+\frac{3}{2}\right)y=11$$

The equation is in standard form.

$$\left(\frac{x^{2}}{4}+\frac{3}{2}\right)y=11$$

Divide both sides by \frac{1}{4}x^{2}+\frac{3}{2}.

$$\frac{\left(\frac{x^{2}}{4}+\frac{3}{2}\right)y}{\frac{x^{2}}{4}+\frac{3}{2}}=\frac{11}{\frac{x^{2}}{4}+\frac{3}{2}}$$

Dividing by \frac{1}{4}x^{2}+\frac{3}{2} undoes the multiplication by \frac{1}{4}x^{2}+\frac{3}{2}.

$$y=\frac{11}{\frac{x^{2}}{4}+\frac{3}{2}}$$

Divide 11 by \frac{1}{4}x^{2}+\frac{3}{2}.

$$y=\frac{44}{x^{2}+6}$$

Variable y cannot be equal to 0.

$$y=\frac{44}{x^{2}+6}\text{, }y\neq 0$$

Solve for y

$$y=\frac{44}{x^{2}+6}$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.

$$\frac{1}{4}y\left(x^{2}+6\right)=9+2$$

Use the distributive property to multiply \frac{1}{4}y by x^{2}+6.

$$\frac{1}{4}yx^{2}+\frac{3}{2}y=9+2$$

Add 9 and 2 to get 11.

$$\frac{1}{4}yx^{2}+\frac{3}{2}y=11$$

Combine all terms containing y.

$$\left(\frac{1}{4}x^{2}+\frac{3}{2}\right)y=11$$

The equation is in standard form.

$$\left(\frac{x^{2}}{4}+\frac{3}{2}\right)y=11$$

Divide both sides by \frac{1}{4}x^{2}+\frac{3}{2}.

$$\frac{\left(\frac{x^{2}}{4}+\frac{3}{2}\right)y}{\frac{x^{2}}{4}+\frac{3}{2}}=\frac{11}{\frac{x^{2}}{4}+\frac{3}{2}}$$

Dividing by \frac{1}{4}x^{2}+\frac{3}{2} undoes the multiplication by \frac{1}{4}x^{2}+\frac{3}{2}.

$$y=\frac{11}{\frac{x^{2}}{4}+\frac{3}{2}}$$

Divide 11 by \frac{1}{4}x^{2}+\frac{3}{2}.

$$y=\frac{44}{x^{2}+6}$$

Variable y cannot be equal to 0.

$$y=\frac{44}{x^{2}+6}\text{, }y\neq 0$$

Solve for x (complex solution)

$$x=-\sqrt{-6+\frac{44}{y}}$$

$$x=\sqrt{-6+\frac{44}{y}}\text{, }y\neq 0$$

Solve for x

$$x=\sqrt{-6+\frac{44}{y}}$$

$$x=-\sqrt{-6+\frac{44}{y}}\text{, }y>0\text{ and }y\leq \frac{22}{3}$$