Solve for A gA+QA=f

$g A + Q A = f$

Factor $A$ out of $g A + Q A$ .

Factor $A$ out of $g A$ .

$A g + Q A = f$

Factor $A$ out of $Q A$ .

$A g + A Q = f$

Factor $A$ out of $A g + A Q$ .

$A (g + Q) = f$

Divide each term in $A (g + Q) = f$ by $g + Q$ and simplify.

Divide each term in $A (g + Q) = f$ by $g + Q$ .

$\frac{A (g + Q)}{g + Q} = \frac{f}{g + Q}$

Simplify the left side.

Cancel the common factor of $g + Q$ .

Cancel the common factor.

$\frac{A (g + Q)}{g + Q} = \frac{f}{g + Q}$

Divide $A$ by $1$ .

$A = \frac{f}{g + Q}$