Solve 5/v=t/8-t

$$\frac { 5 } { v } = \frac { t } { 8 - t }$$

Solve for t

$$t=\frac{40}{v+5}$$

$$v\neq 0\text{ and }v\neq -5$$

Steps for Solving Linear Equation

Variable t cannot be equal to 8 since division by zero is not defined. Multiply both sides of the equation by v\left(t-8\right), the least common multiple of v,8-t.

$$\left(t-8\right)\times 5=-vt$$

Use the distributive property to multiply t-8 by 5.

$$5t-40=-vt$$

Add vt to both sides.

$$5t-40+vt=0$$

Add 40 to both sides. Anything plus zero gives itself.

$$5t+vt=40$$

Combine all terms containing t.

$$\left(5+v\right)t=40$$

The equation is in standard form.

$$\left(v+5\right)t=40$$

Divide both sides by v+5.

$$\frac{\left(v+5\right)t}{v+5}=\frac{40}{v+5}$$

Dividing by v+5 undoes the multiplication by v+5.

$$t=\frac{40}{v+5}$$

Variable t cannot be equal to 8.

$$t=\frac{40}{v+5}\text{, }t\neq 8$$

Solve for v

$$v=-5+\frac{40}{t}$$

$$t\neq 8\text{ and }t\neq 0$$

Steps for Solving Linear Equation

Variable v cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by v\left(t-8\right), the least common multiple of v,8-t.

$$\left(t-8\right)\times 5=-vt$$

Use the distributive property to multiply t-8 by 5.

$$5t-40=-vt$$

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

$$-vt=5t-40$$

The equation is in standard form.

$$\left(-t\right)v=5t-40$$

Divide both sides by -t.

$$\frac{\left(-t\right)v}{-t}=\frac{5t-40}{-t}$$

Dividing by -t undoes the multiplication by -t.

$$v=\frac{5t-40}{-t}$$

Divide -40+5t by -t.

$$v=-5+\frac{40}{t}$$

Variable v cannot be equal to 0.

$$v=-5+\frac{40}{t}\text{, }v\neq 0$$