2 + 3 x = 0 {\displaystyle 2+{{3} \over {x}}=0} Умова: x ≠ 0 {\displaystyle x\neq 0} 2 x + 3 = 0 {\displaystyle 2x+3=0} 2 x = − 3 {\displaystyle 2x=-3} x = − 3 2 = − 1 , 5 {\displaystyle x=-{\frac {3}{2}}=-1,5}
2 − 3 1 , 5 = 0 {\displaystyle 2-{\frac {3}{1,5}}=0} 2 − 30 15 = 0 {\displaystyle 2-{\frac {30}{15}}=0} 2 − 2 = 0 {\displaystyle {2}-{2}=0} 0 = 0 {\displaystyle 0=0}
9 x − 2 = 3 {\displaystyle {\frac {9}{x-2}}=3} Умова: x − 2 ≠ 0 {\displaystyle x-2\neq 0} ; x ≠ 2 {\displaystyle x\neq 2} 9 = 3 ( x − 2 ) {\displaystyle 9=3(x-2)} 3 = x − 2 {\displaystyle 3=x-2} − x = − 2 − 3 {\displaystyle -x=-2-3} x = 2 + 3 {\displaystyle x=2+3} x = 5 {\displaystyle x=5}
9 5 − 2 = 3 {\displaystyle {\frac {9}{5-2}}=3} 9 3 = 3 {\displaystyle {\frac {9}{3}}=3} 3 = 3 {\displaystyle 3=3}
x − 1 x + 5 − 4 = 0 {\displaystyle {\frac {x-1}{x+5}}-4=0} Умова: x + 5 ≠ 0 {\displaystyle x+5\neq 0} ; x ≠ − 5 {\displaystyle x\neq -5} x − 1 − 4 ( x + 5 ) = 0 {\displaystyle x-1-4(x+5)=0} x − 1 − 4 x − 20 = 0 {\displaystyle x-1-4x-20=0} − 3 x − 21 = 0 {\displaystyle -3x-21=0} x + 7 = 0 {\displaystyle x+7=0} x = − 7 {\displaystyle x=-7}
− 7 − 1 − 7 + 5 − 4 = 0 {\displaystyle {\frac {-7-1}{-7+5}}-4=0} 8 2 − 4 = 0 {\displaystyle {\frac {8}{2}}-4=0} 4 − 4 = 0 {\displaystyle 4-4=0} 0 = 0 {\displaystyle 0=0}
6 x + 9 x − 1 = 0 {\displaystyle {\frac {6x+9}{x-1}}=0} Умова: x − 1 ≠ 0 {\displaystyle x-1\neq 0} ; x ≠ − 1 {\displaystyle x\neq -1} 6 x + 9 = 0 {\displaystyle 6x+9=0} 2 x + 3 = 0 {\displaystyle 2x+3=0} 2 x = − 3 {\displaystyle 2x=-3} x = − 3 2 = − 1 , 5 {\displaystyle x=-{\frac {3}{2}}=-1,5}
6 ( − 1 , 5 ) + 9 − 1 , 5 − 1 = 0 {\displaystyle {\frac {6(-1,5)+9}{-1,5-1}}=0} − 9 + 9 − 1 , 5 − 1 = 0 {\displaystyle {\frac {-9+9}{-1,5-1}}=0} 0 = 0 {\displaystyle 0=0}
2 x − 8 3 x 2 = 0 {\displaystyle {\frac {2x-8}{3x^{2}}}=0} Умова: 3 x 2 ≠ 0 {\displaystyle 3x^{2}\neq 0} ; x = 0 {\displaystyle x=0} 2 x − 8 = 0 {\displaystyle 2x-8=0} x − 4 = 0 {\displaystyle x-4=0} x = 4 {\displaystyle x=4}
2 × 4 − 8 3 × 4 2 = 0 {\displaystyle {\frac {2\times 4-8}{3\times 4^{2}}}=0} 8 − 8 3 × 16 = 0 {\displaystyle {\frac {8-8}{3\times 16}}=0} 0 = 0 {\displaystyle 0=0}
3 x − 9 2 x − 6 = 0 {\displaystyle {\frac {3x-9}{2x-6}}=0} Умова: 2 x − 6 ≠ 0 {\displaystyle 2x-6\neq 0} ; x − 3 ≠ 0 {\displaystyle x-3\neq 0} ; x ≠ 3 {\displaystyle x\neq 3} 3 ( x − 3 ) 2 ( x − 3 ) = 0 {\displaystyle {\frac {3(x-3)}{2(x-3)}}=0} 1 , 5 ≠ 0 {\displaystyle 1,5\neq 0} Рівняння не має розв'язків.
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