Solve 2+x(z/+z)=(t+x)z+xz/z

$$2 + x ( z / + z ) = ( t + x ) z + x z / z$$

Solve for t

$$t=-x+\frac{2}{z}$$

$$z\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by z.

$$z\times 2+xz=\left(t+x\right)zz+xz$$

Multiply z and z to get z^{2}.

$$z\times 2+xz=\left(t+x\right)z^{2}+xz$$

Use the distributive property to multiply t+x by z^{2}.

$$z\times 2+xz=tz^{2}+xz^{2}+xz$$

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

$$tz^{2}+xz^{2}+xz=z\times 2+xz$$

Subtract xz^{2} from both sides.

$$tz^{2}+xz=z\times 2+xz-xz^{2}$$

Subtract xz from both sides.

$$tz^{2}=z\times 2+xz-xz^{2}-xz$$

Combine xz and -xz to get 0.

$$tz^{2}=z\times 2-xz^{2}$$

The equation is in standard form.

$$z^{2}t=2z-xz^{2}$$

Divide both sides by z^{2}.

$$\frac{z^{2}t}{z^{2}}=\frac{z\left(2-xz\right)}{z^{2}}$$

Dividing by z^{2} undoes the multiplication by z^{2}.

$$t=\frac{z\left(2-xz\right)}{z^{2}}$$

Divide z\left(2-xz\right) by z^{2}.

$$t=-x+\frac{2}{z}$$

Solve for x

$$x=-t+\frac{2}{z}$$

$$z\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by z.

$$z\times 2+xz=\left(t+x\right)zz+xz$$

Multiply z and z to get z^{2}.

$$z\times 2+xz=\left(t+x\right)z^{2}+xz$$

Use the distributive property to multiply t+x by z^{2}.

$$z\times 2+xz=tz^{2}+xz^{2}+xz$$

Subtract xz^{2} from both sides.

$$z\times 2+xz-xz^{2}=tz^{2}+xz$$

Subtract xz from both sides.

$$z\times 2+xz-xz^{2}-xz=tz^{2}$$

Combine xz and -xz to get 0.

$$z\times 2-xz^{2}=tz^{2}$$

Subtract z\times 2 from both sides.

$$-xz^{2}=tz^{2}-z\times 2$$

The equation is in standard form.

$$\left(-z^{2}\right)x=tz^{2}-2z$$

Divide both sides by -z^{2}.

$$\frac{\left(-z^{2}\right)x}{-z^{2}}=\frac{z\left(tz-2\right)}{-z^{2}}$$

Dividing by -z^{2} undoes the multiplication by -z^{2}.

$$x=\frac{z\left(tz-2\right)}{-z^{2}}$$

Divide z\left(tz-2\right) by -z^{2}.

$$x=-t+\frac{2}{z}$$