Solve F_{x}=F/m(1-t/T)

$$F _ { x } = \frac { F } { m } ( 1 - \frac { t } { T } )$$

Solve for F

$$\left\{\begin{matrix}F=-\frac{F_{x}Tm}{t-T}\text{, }&m\neq 0\text{ and }T\neq 0\text{ and }t\neq T\\F\in \mathrm{R}\text{, }&F_{x}=0\text{ and }T=t\text{ and }m\neq 0\text{ and }t\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by Tm, the least common multiple of m,T.

$$F_{x}Tm=TF\left(1-\frac{t}{T}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{T}{T}.

$$F_{x}Tm=TF\left(\frac{T}{T}-\frac{t}{T}\right)$$

Since \frac{T}{T} and \frac{t}{T} have the same denominator, subtract them by subtracting their numerators.

$$F_{x}Tm=TF\times \frac{T-t}{T}$$

Express T\times \frac{T-t}{T} as a single fraction.

$$F_{x}Tm=\frac{T\left(T-t\right)}{T}F$$

Cancel out T in both numerator and denominator.

$$F_{x}Tm=\left(-t+T\right)F$$

Use the distributive property to multiply -t+T by F.

$$F_{x}Tm=-tF+TF$$

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

$$-tF+TF=F_{x}Tm$$

Combine all terms containing F.

$$\left(-t+T\right)F=F_{x}Tm$$

The equation is in standard form.

$$\left(T-t\right)F=F_{x}Tm$$

Divide both sides by T-t.

$$\frac{\left(T-t\right)F}{T-t}=\frac{F_{x}Tm}{T-t}$$

Dividing by T-t undoes the multiplication by T-t.

$$F=\frac{F_{x}Tm}{T-t}$$

Solve for F_x

$$F_{x}=-\frac{F\left(t-T\right)}{Tm}$$

$$m\neq 0\text{ and }T\neq 0$$