Solve 12y=(x^2-5)^-1

$$12 y = ( x ^ { 2 } - 5 ) ^ { - 1 }$$

Solve for y (complex solution)

$$y=\frac{1}{12\left(x^{2}-5\right)}$$

$$x\neq -\sqrt{5}\text{ and }x\neq \sqrt{5}$$

Steps for Solving Linear Equation

Reorder the terms.

$$12y=\frac{1}{x^{2}-5}$$

Multiply both sides of the equation by x^{2}-5.

$$12y\left(x^{2}-5\right)=1$$

Use the distributive property to multiply 12y by x^{2}-5.

$$12yx^{2}-60y=1$$

Combine all terms containing y.

$$\left(12x^{2}-60\right)y=1$$

Divide both sides by 12x^{2}-60.

$$\frac{\left(12x^{2}-60\right)y}{12x^{2}-60}=\frac{1}{12x^{2}-60}$$

Dividing by 12x^{2}-60 undoes the multiplication by 12x^{2}-60.

$$y=\frac{1}{12x^{2}-60}$$

Divide 1 by 12x^{2}-60.

$$y=\frac{1}{12\left(x^{2}-5\right)}$$

Solve for y

$$y=\frac{1}{12\left(x^{2}-5\right)}$$

$$|x|\neq \sqrt{5}$$

Steps for Solving Linear Equation

Reorder the terms.

$$12y=\frac{1}{x^{2}-5}$$

Multiply both sides of the equation by x^{2}-5.

$$12y\left(x^{2}-5\right)=1$$

Use the distributive property to multiply 12y by x^{2}-5.

$$12yx^{2}-60y=1$$

Combine all terms containing y.

$$\left(12x^{2}-60\right)y=1$$

Divide both sides by 12x^{2}-60.

$$\frac{\left(12x^{2}-60\right)y}{12x^{2}-60}=\frac{1}{12x^{2}-60}$$

Dividing by 12x^{2}-60 undoes the multiplication by 12x^{2}-60.

$$y=\frac{1}{12x^{2}-60}$$

Divide 1 by 12x^{2}-60.

$$y=\frac{1}{12\left(x^{2}-5\right)}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{180+\frac{3}{y}}}{6}$$

$$x=\frac{\sqrt{180+\frac{3}{y}}}{6}\text{, }y\neq 0$$

Solve for x

$$x=\frac{\sqrt{180+\frac{3}{y}}}{6}$$

$$x=-\frac{\sqrt{180+\frac{3}{y}}}{6}\text{, }y\leq -\frac{1}{60}\text{ or }y>0$$