Solve pt-rs=5ts

$$p t - r s = 5 t s$$

Solve for p

$$\left\{\begin{matrix}p=\frac{s\left(r+5t\right)}{t}\text{, }&t\neq 0\\p\in \mathrm{R}\text{, }&\left(s=0\text{ or }r=0\right)\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add rs to both sides.

$$pt=5ts+rs$$

The equation is in standard form.

$$tp=rs+5st$$

Divide both sides by t.

$$\frac{tp}{t}=\frac{s\left(r+5t\right)}{t}$$

Dividing by t undoes the multiplication by t.

$$p=\frac{s\left(r+5t\right)}{t}$$

Solve for r

$$\left\{\begin{matrix}r=\frac{t\left(p-5s\right)}{s}\text{, }&s\neq 0\\r\in \mathrm{R}\text{, }&\left(p=0\text{ or }t=0\right)\text{ and }s=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract pt from both sides.

$$-rs=5ts-pt$$

The equation is in standard form.

$$\left(-s\right)r=5st-pt$$

Divide both sides by -s.

$$\frac{\left(-s\right)r}{-s}=\frac{t\left(5s-p\right)}{-s}$$

Dividing by -s undoes the multiplication by -s.

$$r=\frac{t\left(5s-p\right)}{-s}$$

Divide t\left(5s-p\right) by -s.

$$r=\frac{pt}{s}-5t$$