$\text{a)}$  

$x\ne 0$  

$D=\mathbb{R}-\left\{0\right\}$  

 

$\frac{12}{x}=4\mid \cdot x$  

$12=4x\mid :4$  

$3=x$  

---

$\text{b)}$  

$x^2\ne 0$  

$x\ne 0$  

$D=\mathbb{R}-\left\{0\right\}$  

 

$\frac{16}{x^2}=1\mid \cdot x^2$  

$16=x^2$  

$x=4\text{lub}x=-4$  

$x\in \left\{-4,4\right\}$  

---

$\text{c)}$  

$x-2\ne 0$  

$x\ne 2$  

$D=\mathbb{R}-\left\{2\right\}$  

 

$\frac{x+2}{x-2}=0\mid \cdot \left(x-2\right)$  

$x+2=0\mid -2$  

$x=-2$  

---

$\text{d)}$  

$x+3\ne 0$  

$x\ne -3$  

$D=\mathbb{R}-\left\{-3\right\}$  

 

$\frac{\left(x-1\right)\left(x+5\right)}{x+3}=0\mid \cdot \left(x+3\right)$  

$\left(x-1\right)\left(x+5\right)=0$  

$x-1=0\text{lub}x+5=0$  

$x=1\text{lub}x=-5$  

$x\in \left\{-5,1\right\}$  

---

$\text{e)}$  

$x^2-49\ne 0$  

$x^2\ne 49$  

$x\ne 7\text{i}x\ne -7$  

$D=\mathbb{R}-\left\{-7,7\right\}$  

 

$\frac{x-7}{x^2-49}=0\mid \cdot \left(x^2-49\right)$  

$x-7=0\mid +7$  

$x=7\notin D$  

Brak rozwiązań.

---

$\text{f)}$  

$x\left(x-6\right)\ne 0$  

$x\ne 0\text{i}x-6\ne 0$  

$x\ne 0\text{i}x\ne 6$  

$D=\mathbb{R}-\left\{0,6\right\}$  

 

$\frac{36-x^2}{x\left(x-6\right)}=0\mid \cdot x\left(x-6\right)$  

$36-x^2=0\mid +x^2$  

$36=x^2$  

$x=6\notin D\text{lub}x=-6$  

$x=-6$