Solve y+7/y-3=x

$$\frac { y + 7 } { y - 3 } = x$$

Solve for x

$$x=-\frac{y+7}{3-y}$$

$$y\neq 3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y-3.

$$y+7=x\left(y-3\right)$$

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

$$y+7=xy-3x$$

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

$$xy-3x=y+7$$

Combine all terms containing x.

$$\left(y-3\right)x=y+7$$

Divide both sides by y-3.

$$\frac{\left(y-3\right)x}{y-3}=\frac{y+7}{y-3}$$

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

$$x=\frac{y+7}{y-3}$$

Solve for y

$$y=-\frac{3x+7}{1-x}$$

$$x\neq 1$$

Steps for Solving Linear Equation

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

$$y+7=x\left(y-3\right)$$

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

$$y+7=xy-3x$$

Subtract xy from both sides.

$$y+7-xy=-3x$$

Subtract 7 from both sides.

$$y-xy=-3x-7$$

Combine all terms containing y.

$$\left(1-x\right)y=-3x-7$$

Divide both sides by 1-x.

$$\frac{\left(1-x\right)y}{1-x}=\frac{-3x-7}{1-x}$$

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

$$y=\frac{-3x-7}{1-x}$$

Divide -3x-7 by 1-x.

$$y=-\frac{3x+7}{1-x}$$

Variable y cannot be equal to 3.

$$y=-\frac{3x+7}{1-x}\text{, }y\neq 3$$