Solve d/t-1=-1/u

$$\frac { d } { t } - 1 = - \frac { 1 } { u }$$

Solve for d

$$d=\frac{t\left(u-1\right)}{u}$$

$$t\neq 0\text{ and }u\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by tu, the least common multiple of t,u.

$$ud+tu\left(-1\right)=-t$$

Subtract tu\left(-1\right) from both sides.

$$ud=-t-tu\left(-1\right)$$

Multiply -1 and -1 to get 1.

$$ud=-t+tu$$

The equation is in standard form.

$$ud=tu-t$$

Divide both sides by u.

$$\frac{ud}{u}=\frac{t\left(u-1\right)}{u}$$

Dividing by u undoes the multiplication by u.

$$d=\frac{t\left(u-1\right)}{u}$$

Solve for t

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

Steps for Solving Linear Equation

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

$$ud+tu\left(-1\right)=-t$$

Add t to both sides.

$$ud+tu\left(-1\right)+t=0$$

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

$$tu\left(-1\right)+t=-ud$$

Reorder the terms.

$$-tu+t=-du$$

Combine all terms containing t.

$$\left(-u+1\right)t=-du$$

The equation is in standard form.

$$\left(1-u\right)t=-du$$

Divide both sides by 1-u.

$$\frac{\left(1-u\right)t}{1-u}=-\frac{du}{1-u}$$

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

$$t=-\frac{du}{1-u}$$

Variable t cannot be equal to 0.

$$t=-\frac{du}{1-u}\text{, }t\neq 0$$