Solve y=1/x-3+2

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

Solve for x

$$x=-\frac{3y-5}{2-y}$$

$$y\neq 2$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by x-3.

$$y\left(x-3\right)=1+\left(x-3\right)\times 2$$

Use the distributive property to multiply y by x-3.

$$yx-3y=1+\left(x-3\right)\times 2$$

Use the distributive property to multiply x-3 by 2.

$$yx-3y=1+2x-6$$

Subtract 6 from 1 to get -5.

$$yx-3y=-5+2x$$

Subtract 2x from both sides.

$$yx-3y-2x=-5$$

Add 3y to both sides.

$$yx-2x=-5+3y$$

Combine all terms containing x.

$$\left(y-2\right)x=-5+3y$$

The equation is in standard form.

$$\left(y-2\right)x=3y-5$$

Divide both sides by y-2.

$$\frac{\left(y-2\right)x}{y-2}=\frac{3y-5}{y-2}$$

Dividing by y-2 undoes the multiplication by y-2.

$$x=\frac{3y-5}{y-2}$$

Variable x cannot be equal to 3.

$$x=\frac{3y-5}{y-2}\text{, }x\neq 3$$

Solve for y

$$y=-\frac{5-2x}{x-3}$$

$$x\neq 3$$