Solve 4(x^2-2)y=-2x^2+6

$$4 ( x ^ { 2 } - 2 ) y = - 2 x ^ { 2 } + 6$$

Solve for y (complex solution)

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

$$x\neq -\sqrt{2}\text{ and }x\neq \sqrt{2}$$

Steps for Solving Linear Equation

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

$$\left(4x^{2}-8\right)y=-2x^{2}+6$$

The equation is in standard form.

$$\left(4x^{2}-8\right)y=6-2x^{2}$$

Divide both sides by 4x^{2}-8.

$$\frac{\left(4x^{2}-8\right)y}{4x^{2}-8}=\frac{6-2x^{2}}{4x^{2}-8}$$

Dividing by 4x^{2}-8 undoes the multiplication by 4x^{2}-8.

$$y=\frac{6-2x^{2}}{4x^{2}-8}$$

Divide -2x^{2}+6 by 4x^{2}-8.

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

Solve for y

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

$$|x|\neq \sqrt{2}$$

Steps for Solving Linear Equation

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

$$\left(4x^{2}-8\right)y=-2x^{2}+6$$

The equation is in standard form.

$$\left(4x^{2}-8\right)y=6-2x^{2}$$

Divide both sides by 4x^{2}-8.

$$\frac{\left(4x^{2}-8\right)y}{4x^{2}-8}=\frac{6-2x^{2}}{4x^{2}-8}$$

Dividing by 4x^{2}-8 undoes the multiplication by 4x^{2}-8.

$$y=\frac{6-2x^{2}}{4x^{2}-8}$$

Divide -2x^{2}+6 by 4x^{2}-8.

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

Solve for x (complex solution)

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

$$x=i\left(2y+1\right)^{-\frac{1}{2}}\sqrt{-4y-3}\text{, }y\neq -\frac{1}{2}$$

Solve for x

$$x=\sqrt{\frac{4y+3}{2y+1}}$$

$$x=-\sqrt{\frac{4y+3}{2y+1}}\text{, }y\leq -\frac{3}{4}\text{ or }y>-\frac{1}{2}$$