Solve -y/12.5=-1/25+y/u

$$- \frac { y } { 12.5 } = - \frac { 1 } { 25 } + \frac { y } { u }$$

Solve for u

$$u=-\frac{25y}{2y-1}$$

$$y\neq 0\text{ and }y\neq \frac{1}{2}$$

Steps for Solving Linear Equation

Variable u cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 25u, the least common multiple of 25,u.

$$-25u\times \frac{y}{12.5}=25u\left(-\frac{1}{25}\right)+25y$$

Multiply 25 and -\frac{1}{25} to get -1.

$$-25u\times \frac{y}{12.5}=-u+25y$$

Add u to both sides.

$$-25u\times \frac{y}{12.5}+u=25y$$

Combine all terms containing u.

$$\left(-25\times \frac{y}{12.5}+1\right)u=25y$$

The equation is in standard form.

$$\left(1-2y\right)u=25y$$

Divide both sides by -2y+1.

$$\frac{\left(1-2y\right)u}{1-2y}=\frac{25y}{1-2y}$$

Dividing by -2y+1 undoes the multiplication by -2y+1.

$$u=\frac{25y}{1-2y}$$

Variable u cannot be equal to 0.

$$u=\frac{25y}{1-2y}\text{, }u\neq 0$$

Solve for y

$$y=\frac{u}{2u+25}$$

$$u\neq -\frac{25}{2}\text{ and }u\neq 0$$