Solve v-u/a=+(u)

$$\frac { v - u } { a } = + ( u )$$

Solve for a

$$\left\{\begin{matrix}a=\frac{v}{u}-1\text{, }&v\neq u\text{ and }u\neq 0\\a\neq 0\text{, }&u=0\text{ and }v=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$v-u=ua$$

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

$$ua=v-u$$

Divide both sides by u.

$$\frac{ua}{u}=\frac{v-u}{u}$$

Dividing by u undoes the multiplication by u.

$$a=\frac{v-u}{u}$$

Divide v-u by u.

$$a=\frac{v}{u}-1$$

Variable a cannot be equal to 0.

$$a=\frac{v}{u}-1\text{, }a\neq 0$$

Solve for u

$$\left\{\begin{matrix}u=\frac{v}{a+1}\text{, }&a\neq -1\text{ and }a\neq 0\\u\in \mathrm{R}\text{, }&a=-1\text{ and }v=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

$$v-u=ua$$

Subtract ua from both sides.

$$v-u-ua=0$$

Subtract v from both sides. Anything subtracted from zero gives its negation.

$$-u-ua=-v$$

Combine all terms containing u.

$$\left(-1-a\right)u=-v$$

The equation is in standard form.

$$\left(-a-1\right)u=-v$$

Divide both sides by -1-a.

$$\frac{\left(-a-1\right)u}{-a-1}=-\frac{v}{-a-1}$$

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

$$u=-\frac{v}{-a-1}$$

Divide -v by -1-a.

$$u=\frac{v}{a+1}$$