Solve x/x-5=y/3

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

Solve for x

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

$$y\neq 3$$

Steps for Solving Linear Equation

Variable x cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by 3\left(x-5\right), the least common multiple of x-5,3.

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

Use the distributive property to multiply x-5 by y.

$$3x=xy-5y$$

Subtract xy from both sides.

$$3x-xy=-5y$$

Combine all terms containing x.

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

Divide both sides by -y+3.

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

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

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

Variable x cannot be equal to 5.

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

Solve for y

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

$$x\neq 5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3\left(x-5\right), the least common multiple of x-5,3.

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

Use the distributive property to multiply x-5 by y.

$$3x=xy-5y$$

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

$$xy-5y=3x$$

Combine all terms containing y.

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

Divide both sides by x-5.

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

Dividing by x-5 undoes the multiplication by x-5.

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