Solve y=2u/3-u

$$y = \frac { 2 u } { 3 - u }$$

Solve for u

$$u=\frac{3y}{y+2}$$

$$y\neq -2$$

Steps for Solving Linear Equation

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

$$y\left(-u+3\right)=2u$$

Use the distributive property to multiply y by -u+3.

$$-yu+3y=2u$$

Subtract 2u from both sides.

$$-yu+3y-2u=0$$

Subtract 3y from both sides. Anything subtracted from zero gives its negation.

$$-yu-2u=-3y$$

Combine all terms containing u.

$$\left(-y-2\right)u=-3y$$

Divide both sides by -y-2.

$$\frac{\left(-y-2\right)u}{-y-2}=-\frac{3y}{-y-2}$$

Dividing by -y-2 undoes the multiplication by -y-2.

$$u=-\frac{3y}{-y-2}$$

Divide -3y by -y-2.

$$u=\frac{3y}{y+2}$$

Variable u cannot be equal to 3.

$$u=\frac{3y}{y+2}\text{, }u\neq 3$$

Solve for y

$$y=\frac{2u}{3-u}$$

$$u\neq 3$$