Solve 0=(1+xt+x)

$$0 = ( 1 + x t + x )$$

Solve for t

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

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$1+xt+x=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$xt+x=-1$$

Subtract x from both sides.

$$xt=-1-x$$

The equation is in standard form.

$$xt=-x-1$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Divide -1-x by x.

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

Solve for x

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

$$t\neq -1$$

Steps for Solving Linear Equation

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

$$1+xt+x=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$xt+x=-1$$

Combine all terms containing x.

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

Divide both sides by t+1.

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

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

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