133 Вправа 133Алгебра 8 клас Бевз 2025 · § 3 · стор. 30

133. Розв’яжи рівняння.

а) ${\displaystyle \frac{2x-3}{5x}=}$${\displaystyle 0}$;

${\displaystyle \{\begin{array}{rl}& 2x-3=0\\ & 5x\ne 0\end{array}}$;

${\displaystyle \{\begin{array}{rl}& x=1,5\\ & x\ne 0\end{array}}$;

${\displaystyle x=}$${\displaystyle 1,5}$;

б) ${\displaystyle \frac{15-3x}{x+4}=}$${\displaystyle 0}$;

${\displaystyle \{\begin{array}{rl}& 15-3x=0\\ & x+4\ne 0\end{array}}$;

${\displaystyle \{\begin{array}{rl}& x=5\\ & x\ne -4\end{array}}$;

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

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

${\displaystyle \{\begin{array}{rl}& {(x-1)}^2=0\\ & (1-x)(1+x)\ne 0\end{array}}$;

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

коренів немає;

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

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

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

коренів немає.