Solve 1/x+1/t=1

$$\frac{ 1 }{ x } + \frac{ 1 }{ t } = 1$$

Solve for t

$$t=-\frac{x}{1-x}$$

$$x\neq 0\text{ and }x\neq 1$$

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 tx, the least common multiple of x,t.

$$t+x=tx$$

Subtract tx from both sides.

$$t+x-tx=0$$

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

$$t-tx=-x$$

Combine all terms containing t.

$$\left(1-x\right)t=-x$$

Divide both sides by 1-x.

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

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

$$t=-\frac{x}{1-x}$$

Variable t cannot be equal to 0.

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

Solve for x

$$x=-\frac{t}{1-t}$$

$$t\neq 0\text{ and }t\neq 1$$

Steps for Solving Linear Equation

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

$$t+x=tx$$

Subtract tx from both sides.

$$t+x-tx=0$$

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

$$x-tx=-t$$

Combine all terms containing x.

$$\left(1-t\right)x=-t$$

Divide both sides by 1-t.

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

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

$$x=-\frac{t}{1-t}$$

Variable x cannot be equal to 0.

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