1294 Вправа 1294Алгебра 8 клас Бевз 2025 · § 26 · стор. 251

1294. Спрости вираз. а) 4a/(a − b) + 2b/(a + b) − 1; б) x/(x − z) + 3x/(x + z) − 2xz/(x² − z²).

Спільний знаменник ${\displaystyle (a-b)(a+b)=}$${\displaystyle a^2-b^2}$.

а) ${\displaystyle \frac{{4a}^{\mathrm{\setminus }a+b}}{a-b}+\frac{{2b}^{\mathrm{\setminus }a-b}}{a+b}-1^{\mathrm{\setminus }{a}^2-b^2}}$=

=${\displaystyle \frac{4a^2+4ab+2ab-2b^2-a^2+b^2}{a^2-b^2}=}$${\displaystyle \frac{3a^2+6ab-b^2}{a^2-b^2}}$;

б) ${\displaystyle x^2-z^2=}$${\displaystyle (x-z)(x+z)}$;

${\displaystyle \frac{x^{\mathrm{\setminus }x+z}}{x-z}+\frac{{3x}^{\mathrm{\setminus }x-z}}{x+z}-\frac{2xz}{(x-z)(x+z)}}$=

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

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