123 Вправа 123Алгебра 8 клас Бевз 2025 · § 3 · стор. 29

123. Solve the equation.

a) ${\displaystyle \frac{x^2}{x+2}=}$${\displaystyle 0}$;

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

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

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

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

${\displaystyle x^2+4>0}$; ${\displaystyle x-2=}$${\displaystyle 0}$; ${\displaystyle x=}$${\displaystyle 2}$;

c) ${\displaystyle \frac{x^2-25}{{(x+5)}^2}=}$${\displaystyle 0}$;

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

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

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

d) ${\displaystyle \frac{2x^2-10x}{x(x+5)}=}$${\displaystyle 0}$;

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

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

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

Answer: a) 0; b) 2; c) 5; d) 5.