Solve 8/y-1=x+1/4

$$\frac { 8 } { y - 1 } = \frac { x + 1 } { 4 }$$

Solve for x

$$x=-\frac{33-y}{1-y}$$

$$y\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4\left(y-1\right), the least common multiple of y-1,4.

$$4\times 8=\left(y-1\right)\left(x+1\right)$$

Multiply 4 and 8 to get 32.

$$32=\left(y-1\right)\left(x+1\right)$$

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

$$32=yx+y-x-1$$

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

$$yx+y-x-1=32$$

Subtract y from both sides.

$$yx-x-1=32-y$$

Add 1 to both sides.

$$yx-x=32-y+1$$

Add 32 and 1 to get 33.

$$yx-x=33-y$$

Combine all terms containing x.

$$\left(y-1\right)x=33-y$$

Divide both sides by y-1.

$$\frac{\left(y-1\right)x}{y-1}=\frac{33-y}{y-1}$$

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

$$x=\frac{33-y}{y-1}$$

Solve for y

$$y=\frac{x+33}{x+1}$$

$$x\neq -1$$

Steps for Solving Linear Equation

Variable y cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 4\left(y-1\right), the least common multiple of y-1,4.

$$4\times 8=\left(y-1\right)\left(x+1\right)$$

Multiply 4 and 8 to get 32.

$$32=\left(y-1\right)\left(x+1\right)$$

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

$$32=yx+y-x-1$$

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

$$yx+y-x-1=32$$

Add x to both sides.

$$yx+y-1=32+x$$

Add 1 to both sides.

$$yx+y=32+x+1$$

Add 32 and 1 to get 33.

$$yx+y=33+x$$

Combine all terms containing y.

$$\left(x+1\right)y=33+x$$

The equation is in standard form.

$$\left(x+1\right)y=x+33$$

Divide both sides by x+1.

$$\frac{\left(x+1\right)y}{x+1}=\frac{x+33}{x+1}$$

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

$$y=\frac{x+33}{x+1}$$

Variable y cannot be equal to 1.

$$y=\frac{x+33}{x+1}\text{, }y\neq 1$$