Solve y=4/x-1-1

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

Solve for x

$$x=\frac{y+5}{y+1}$$

$$y\neq -1$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by x-1.

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

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

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

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

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

Add 4 and 1 to get 5.

$$yx-y=5-x$$

Add x to both sides.

$$yx-y+x=5$$

Add y to both sides.

$$yx+x=5+y$$

Combine all terms containing x.

$$\left(y+1\right)x=5+y$$

The equation is in standard form.

$$\left(y+1\right)x=y+5$$

Divide both sides by y+1.

$$\frac{\left(y+1\right)x}{y+1}=\frac{y+5}{y+1}$$

Dividing by y+1 undoes the multiplication by y+1.

$$x=\frac{y+5}{y+1}$$

Variable x cannot be equal to 1.

$$x=\frac{y+5}{y+1}\text{, }x\neq 1$$

Solve for y

$$y=-\frac{x-5}{x-1}$$

$$x\neq 1$$