Solve (sinx^2)^2/x^2-x=y

$$\frac { ( \sin x ^ { 2 } ) ^ { 2 } } { x ^ { 2 } - x } = y$$

Solve for y (complex solution)

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

$$x\neq 1\text{ and }x\neq 0$$

Steps for Solving Linear Equation

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

$$\left(\sin(x^{2})\right)^{2}=yx\left(x-1\right)$$

Use the distributive property to multiply yx by x-1.

$$\left(\sin(x^{2})\right)^{2}=yx^{2}-yx$$

Swap sides so that all variable terms are on the left hand side.

$$yx^{2}-yx=\left(\sin(x^{2})\right)^{2}$$

Combine all terms containing y.

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

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

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

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

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

Divide \left(\sin(x^{2})\right)^{2} by x^{2}-x.

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

Solve for y

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

$$x\neq 1\text{ and }x\neq 0$$

Steps for Solving Linear Equation

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

$$\left(\sin(x^{2})\right)^{2}=yx\left(x-1\right)$$

Use the distributive property to multiply yx by x-1.

$$\left(\sin(x^{2})\right)^{2}=yx^{2}-yx$$

Swap sides so that all variable terms are on the left hand side.

$$yx^{2}-yx=\left(\sin(x^{2})\right)^{2}$$

Combine all terms containing y.

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

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

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

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

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

Divide \left(\sin(x^{2})\right)^{2} by x^{2}-x.

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