193 Вправа 193Алгебра 8 клас Бевз 2025 · § 4 · стор. 40

193. Знайди значення виразу.

а) ${\displaystyle \frac{x-3}{x^2+3x}-\frac{x+3}{x^2-3x}-\frac{4x}{x^2-9}}$=

=${\displaystyle \frac{{x-3}^{\mathrm{\setminus }x-3}}{x(x+3)}-\frac{{x+3}^{\mathrm{\setminus }x+3}}{x(x-3)}-\frac{{4x}^{\mathrm{\setminus }x}}{(x-3)(x+3)}}$=

=${\displaystyle \frac{(x-3)(x-3)-(x+3)(x+3)-4x^2}{x(x-3)(x+3)}}$=

=${\displaystyle \frac{x^2-6x+9-x^2-6x-9-4x^2}{x(x-3)(x+3)}=}$${\displaystyle \frac{-4x^2-12x}{x(x-3)(x+3)}}$=

=${\displaystyle \frac{-4\cancel{x\left(x+3\right)}}{(x-3)\cancel{x\left(x+3\right)}}=}$${\displaystyle -\frac{4}{x-3}}$;

якщо x = 7, то ${\displaystyle -\frac{4}{7-3}=}$${\displaystyle -1}$;

б) ${\displaystyle \frac{x+1}{x-1}-\frac{x-1}{x+1}-\frac{4}{x^2-1}}$=

=${\displaystyle \frac{{x+1}^{\mathrm{\setminus }x+1}}{x-1}-\frac{{x-1}^{\mathrm{\setminus }x-1}}{x+1}-\frac{4}{(x-1)(x+1)}}$=

=${\displaystyle \frac{(x+1)(x+1)-(x-1)(x-1)-4}{(x-1)(x+1)}}$=

=${\displaystyle \frac{x^2+2x+1-x^2+2x-1-4}{(x-1)(x+1)}=}$${\displaystyle \frac{4x-4}{(x-1)(x+1)}}$=

=${\displaystyle \frac{4\cancel{\left(x-1\right)}}{(x+1)\cancel{\left(x-1\right)}}=}$${\displaystyle \frac{4}{x+1}}$;

якщо x = −2, то ${\displaystyle \frac{4}{(-2)+1}=}$${\displaystyle -4}$.