Solve w/H=1-T/t

$$\frac { w } { H } = 1 - \frac { T } { t }$$

Solve for H

$$\left\{\begin{matrix}H=-\frac{tw}{T-t}\text{, }&t\neq 0\text{ and }w\neq 0\text{ and }T\neq t\\H\neq 0\text{, }&t=T\text{ and }w=0\text{ and }T\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable H cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by Ht, the least common multiple of H,t.

$$tw=Ht-HT$$

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

$$Ht-HT=tw$$

Combine all terms containing H.

$$\left(t-T\right)H=tw$$

Divide both sides by t-T.

$$\frac{\left(t-T\right)H}{t-T}=\frac{tw}{t-T}$$

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

$$H=\frac{tw}{t-T}$$

Variable H cannot be equal to 0.

$$H=\frac{tw}{t-T}\text{, }H\neq 0$$

Solve for T

$$T=\frac{t\left(H-w\right)}{H}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by Ht, the least common multiple of H,t.

$$tw=Ht-HT$$

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

$$Ht-HT=tw$$

Subtract Ht from both sides.

$$-HT=tw-Ht$$

The equation is in standard form.

$$\left(-H\right)T=tw-Ht$$

Divide both sides by -H.

$$\frac{\left(-H\right)T}{-H}=\frac{t\left(w-H\right)}{-H}$$

Dividing by -H undoes the multiplication by -H.

$$T=\frac{t\left(w-H\right)}{-H}$$

Divide t\left(w-H\right) by -H.

$$T=-\frac{tw}{H}+t$$