Solve t*23=t*1s+17s

$$t \cdot 23 = t \cdot 1 s + 17 s$$

Solve for s

$$s=\frac{23t}{t+17}$$

$$t\neq -17$$

Steps for Solving Linear Equation

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

$$t\times 1s+17s=t\times 23$$

Reorder the terms.

$$st+17s=23t$$

Combine all terms containing s.

$$\left(t+17\right)s=23t$$

Divide both sides by 17+t.

$$\frac{\left(t+17\right)s}{t+17}=\frac{23t}{t+17}$$

Dividing by 17+t undoes the multiplication by 17+t.

$$s=\frac{23t}{t+17}$$

Solve for t

$$t=\frac{17s}{23-s}$$

$$s\neq 23$$

Steps for Solving Linear Equation

Subtract t\times 1s from both sides.

$$t\times 23-t\times 1s=17s$$

Reorder the terms.

$$23t-st=17s$$

Reorder the terms.

$$-st+23t=17s$$

Combine all terms containing t.

$$\left(-s+23\right)t=17s$$

The equation is in standard form.

$$\left(23-s\right)t=17s$$

Divide both sides by 23-s.

$$\frac{\left(23-s\right)t}{23-s}=\frac{17s}{23-s}$$

Dividing by 23-s undoes the multiplication by 23-s.

$$t=\frac{17s}{23-s}$$