Solve cos(x)+y/y=x

$$\frac { \cos ( x ) + y } { y } = x$$

Solve for y

$$y=-\frac{\cos(x)}{1-x}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}\text{ and }x\neq 1$$

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.

$$\cos(x)+y=xy$$

Subtract xy from both sides.

$$\cos(x)+y-xy=0$$

Subtract \cos(x) from both sides. Anything subtracted from zero gives its negation.

$$y-xy=-\cos(x)$$

Combine all terms containing y.

$$\left(1-x\right)y=-\cos(x)$$

Divide both sides by 1-x.

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

Dividing by 1-x undoes the multiplication by 1-x.

$$y=-\frac{\cos(x)}{1-x}$$

Variable y cannot be equal to 0.

$$y=-\frac{\cos(x)}{1-x}\text{, }y\neq 0$$