369 Вправа 369Алгебра 8 клас Бевз 2025 · § 8 · стор. 76

369. Розв’яжи рівняння.

а) ${\displaystyle \frac{x+3}{x}-\frac{2^{\mathrm{\setminus }x}}{1}=}$${\displaystyle 0}$;

${\displaystyle \frac{x+3-2x}{x}=}$${\displaystyle \frac{3-x}{x}}$=0;

${\displaystyle \{\begin{array}{rl}& 3-x=0\\ & x\ne 0\end{array}}$;

${\displaystyle \{\begin{array}{rl}& x=3\\ & x\ne 0\end{array}}$;

${\displaystyle x=}$${\displaystyle 3}$;

б) ${\displaystyle \frac{2x-1}{3x}=}$${\displaystyle 0}$;

${\displaystyle \{\begin{array}{rl}& 2x-1=0\\ & 3x\ne 0\end{array}}$;

${\displaystyle \{\begin{array}{rl}& x=\frac{1}{2}\\ & x\ne 0\end{array}}$;

${\displaystyle x=}$${\displaystyle 0,5}$;

в) ${\displaystyle \frac{x}{x+2}-\frac{2^{\mathrm{\setminus }x+2}}{1}=}$${\displaystyle 0}$;

${\displaystyle \frac{x-2(x+2)}{x+2}=}$${\displaystyle \frac{x-2x-4}{x+2}=}$${\displaystyle \frac{-x-4}{x+2}}$=0;

${\displaystyle \{\begin{array}{rl}& -x-4=0\\ & x+2\ne 0\end{array}}$;

${\displaystyle \{\begin{array}{rl}& x=-4\\ & x\ne -2\end{array}}$;

${\displaystyle x=}$${\displaystyle -4}$;

г) ${\displaystyle \frac{x-8}{x}=}$${\displaystyle 3}$;

${\displaystyle \frac{x-8}{x}-\frac{3^{\mathrm{\setminus }x}}{1}=}$${\displaystyle 0}$;

${\displaystyle \frac{x-8-3x}{x}=}$${\displaystyle \frac{-2x-8}{x}}$=0;

${\displaystyle \{\begin{array}{rl}& -2x-8=0\\ & x\ne 0\end{array}}$;

${\displaystyle \{\begin{array}{rl}& x=-4\\ & x\ne 0\end{array}}$;

${\displaystyle x=}$${\displaystyle -4}$;

ґ) ${\displaystyle \frac{5-x}{x}=}$${\displaystyle 6}$;

${\displaystyle \frac{5-x}{x}-\frac{6^{\mathrm{\setminus }x}}{1}=}$${\displaystyle 0}$;

${\displaystyle \frac{5-x-6x}{x}=}$${\displaystyle \frac{5-7x}{x}}$=0;

${\displaystyle \{\begin{array}{rl}& 5-7x=0\\ & x\ne 0\end{array}}$;

${\displaystyle \{\begin{array}{rl}& x=\frac{5}{7}\\ & x\ne 0\end{array}}$;

${\displaystyle x=}$${\displaystyle \frac{5}{7}}$;

д) ${\displaystyle \frac{x}{x-2}=}$${\displaystyle 2}$;

${\displaystyle \frac{x}{x-2}-\frac{2^{\mathrm{\setminus }x-2}}{1}=}$${\displaystyle 0}$;

${\displaystyle \frac{x-2(x-2)}{x-2}=}$${\displaystyle \frac{x-2x+4}{x-2}=}$${\displaystyle \frac{4-x}{x-2}}$=0;

${\displaystyle \{\begin{array}{rl}& 4-x=0\\ & x-2\ne 0\end{array}}$;

${\displaystyle \{\begin{array}{rl}& x=4\\ & x\ne 2\end{array}}$;

${\displaystyle x=}$${\displaystyle 4}$.