Solve for g gh-gt+g=t

$g h - g t + g = t$

Factor $g$ out of $g h - g t + g$ .

Factor $g$ out of $g h$ .

$g (h) - g t + g = t$

Factor $g$ out of $- g t$ .

$g (h) + g (- 1 t) + g = t$

Raise $g$ to the power of $1$ .

$g (h) + g (- 1 t) + g = t$

Factor $g$ out of $g^{1}$ .

$g (h) + g (- 1 t) + g \cdot 1 = t$

Factor $g$ out of $g (h) + g (- 1 t)$ .

$g (h - 1 t) + g \cdot 1 = t$

Factor $g$ out of $g (h - 1 t) + g \cdot 1$ .

$g (h - 1 t + 1) = t$

Rewrite $- 1 t$ as $- t$ .

$g (h - t + 1) = t$

Divide each term in $g (h - t + 1) = t$ by $h - t + 1$ and simplify.

Divide each term in $g (h - t + 1) = t$ by $h - t + 1$ .

$\frac{g (h - t + 1)}{h - t + 1} = \frac{t}{h - t + 1}$

Simplify the left side.

Cancel the common factor of $h - t + 1$ .

Cancel the common factor.

$\frac{g (h - t + 1)}{h - t + 1} = \frac{t}{h - t + 1}$

Divide $g$ by $1$ .

$g = \frac{t}{h - t + 1}$