$\text{a)}$

Zał:

$x+1\ne 0$  

$x\ne -1$  

 

$\frac{6}{x+1}=4\mid \cdot \left(x+1\right)$

$6=4\left(x+1\right)$

$6=4x+4\mid -4$

$2=4x\mid :4$

$\frac{2}{4}=x$  

$\frac{1}{2}=x$  

---

$\text{b)}$

Zał:

$x\ne 0$  

 

$\frac{3x+2}{x}=5\mid \cdot x$

$3x+2=5x\mid -3x$

$2=2x\mid :2$

$1=x$

---

$\text{c)}$  

Zał:

$-2x+7\ne 0$  

$7\ne 2x$  

$\frac{7}{2}\ne x$  

 

$\frac{3}{-2x+7}=1\mid \cdot \left(-2x+7\right)$

$3=-2x+7\mid -7$

$-4=-2x\mid :\left(-2\right)$

$2=x$

---

$\text{d)}$  

Zał:

$x-1\ne 0$  

$x\ne 1$  

 

$\frac{2x}{x-1}=3\mid \cdot \left(x-1\right)$

$2x=3x-3\mid -3x$

$-x=-3\mid \cdot \left(-1\right)$

$x=3$

---

$\text{e)}$  

Zał:

$1-3x\ne 0$  

$1\ne 3x$  

$\frac{1}{3}\ne x$  

 

$\frac{7x+6}{1-3x}=-4\mid \cdot \left(1-3x\right)$

$7x+6=-4\left(1-3x\right)$

$7x+6=-4+12x\mid -12x$

$-5x+6=-4\mid -6$  

$-5x=-10\mid :\left(-5\right)$  

$x=2$  

---

$\text{f)}$  

Zał:

$4-x\ne 0$  

$4\ne x$  

 

$\frac{4-2x}{4-x}=-2\mid \cdot \left(4-x\right)$

$4-2x=-2\left(4-x\right)$

$4-2x=-8+2x\mid -2x$

$4-4x=-8\mid -4$   

$-4x=-12\mid :\left(-4\right)$  

$x=3$

---

$\text{g)}$  

Zał:

$3x+1\ne 0$  

$3x\ne -1$  

$x\ne -\frac{1}{3}$  

 

$\frac{x-5}{3x+1}-2=0\mid +2$

$\frac{x-5}{3x+1}=2\mid \cdot \left(3x+1\right)$

$x-5=2\left(3x+1\right)$

$x-5=6x+2\mid -6x$

$-5x-5=2\mid +5$

$-5x=7\mid :\left(-5\right)$

$x=-\frac{7}{5}$

$x=-1\frac{2}{5}$  

---

$\text{h)}$

Zał:

$x-1\ne 0$  

$x\ne 1$  

 

$\frac{2x+4}{x-1}+4=0\mid -4$

$\frac{2x+4}{x-1}=-4\mid \cdot \left(x-1\right)$

$2x+4=-4\left(x-1\right)$

$2x+4=-4x+4\mid -4$

$2x=-4x\mid +4x$

$6x=0\mid :6$

$x=0$