a)   $\frac{1}{A+B}+1=\frac{1}{C}$  

$\frac{1}{A+B}=\frac{1}{C}-1$  

$\frac{1}{A+B}=\frac{1}{C}-\frac{\mathbf{C}}{C}$  

$\frac{1}{A+B}=\frac{1-\mathbf{C}}{C}$  

$\left(A+B\right)\left(1-\mathbf{C}\right)=\mathbf{C}\mid :\left(1-\mathbf{C}\right)$  

$A+B=\frac{\mathbf{C}}{1-\mathbf{C}}$  

$A=\frac{\mathbf{C}}{1-\mathbf{C}}-\mathbf{B}$  

Założenia:

$A+B\ne 0,C\ne 0\text{i}C\ne 1$  

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b)   $\frac{1}{A}-1=\frac{B}{C}$  

$\frac{1}{\mathbf{A}}=\frac{\mathbf{B}}{\mathbf{C}}+1$  

$\frac{1}{\mathbf{A}}=\frac{\mathbf{B}}{\mathbf{C}}+\frac{\mathbf{C}}{\mathbf{C}}$  

$\frac{1}{\mathbf{A}}=\frac{\mathbf{B}+\mathbf{C}}{\mathbf{C}}$  

$\mathbf{A}\left(\mathbf{B}+\mathbf{C}\right)=\mathbf{C}\mid :\left(\mathbf{B}+\mathbf{C}\right)$  

$\mathbf{A}=\frac{\mathbf{C}}{\mathbf{B}+\mathbf{C}}$  

Założenia:

$\mathbf{A}\ne 0,\mathbf{C}\ne 0\text{i}\mathbf{C}\ne -\mathbf{B}$