Solve y=1/x-4+3

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

Solve for x

$$x=-\frac{4y-11}{3-y}$$

$$y\neq 3$$

Steps for Solving Linear Equation

Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by x-4.

$$y\left(x-4\right)=1+\left(x-4\right)\times 3$$

Use the distributive property to multiply y by x-4.

$$yx-4y=1+\left(x-4\right)\times 3$$

Use the distributive property to multiply x-4 by 3.

$$yx-4y=1+3x-12$$

Subtract 12 from 1 to get -11.

$$yx-4y=-11+3x$$

Subtract 3x from both sides.

$$yx-4y-3x=-11$$

Add 4y to both sides.

$$yx-3x=-11+4y$$

Combine all terms containing x.

$$\left(y-3\right)x=-11+4y$$

The equation is in standard form.

$$\left(y-3\right)x=4y-11$$

Divide both sides by y-3.

$$\frac{\left(y-3\right)x}{y-3}=\frac{4y-11}{y-3}$$

Dividing by y-3 undoes the multiplication by y-3.

$$x=\frac{4y-11}{y-3}$$

Variable x cannot be equal to 4.

$$x=\frac{4y-11}{y-3}\text{, }x\neq 4$$

Solve for y

$$y=-\frac{11-3x}{x-4}$$

$$x\neq 4$$