Solve L/varepsilon=0I-xz/t+xs

$$\frac { L } { \varepsilon } = \frac { 0 I - x z } { t + x s }$$

Solve for L

$$L=-\frac{xz\epsilon }{sx+t}$$

$$\epsilon \neq 0\text{ and }t\neq -sx$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \epsilon \left(sx+t\right), the least common multiple of \epsilon ,t+xs.

$$\left(sx+t\right)L=\epsilon \left(0I-xz\right)$$

Use the distributive property to multiply sx+t by L.

$$sxL+tL=\epsilon \left(0I-xz\right)$$

Anything times zero gives zero.

$$sxL+tL=\epsilon \left(0-xz\right)$$

Anything plus zero gives itself.

$$sxL+tL=\epsilon \left(-1\right)xz$$

Combine all terms containing L.

$$\left(sx+t\right)L=\epsilon \left(-1\right)xz$$

The equation is in standard form.

$$\left(sx+t\right)L=-xz\epsilon$$

Divide both sides by t+xs.

$$\frac{\left(sx+t\right)L}{sx+t}=-\frac{xz\epsilon }{sx+t}$$

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

$$L=-\frac{xz\epsilon }{sx+t}$$