177 Вправа 177Алгебра 8 клас Бевз 2025 · § 4 · стор. 38

Умова

Спрости вираз.

177. Спрости вираз.

а) $\frac{2 a + c}{a - c} + \frac{3 c}{c - a} =$ $\frac{2 a + c}{a - c} - \frac{3 c}{a - c} =$ $\frac{2 a + c - 3 c}{a - c}$ =

= $\frac{2 a - 2 c}{a - c} =$ $\frac{2 (a - c)}{(a - c)} =$ $2$ ;

б) $\frac{2 x}{x - 2} + \frac{x + 2}{2 - x} =$ $\frac{2 x}{x - 2} - \frac{x + 2}{x - 2} =$ $\frac{2 x - (x + 2)}{x - 2}$ =

= $\frac{2 x - x - 2}{x - 2} =$ $\frac{(x - 2)}{(x - 2)} =$ $1$ ;

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

= $\frac{(x - 1) (x - 1)}{(x - 1)} =$ $x - 1$ ;

г) $\frac{a}{4 a^{2} - 9} - \frac{a + 3}{9 - 4 a^{2}} =$ $\frac{a}{(2 a - 3) (2 a + 3)} + \frac{a + 3}{(2 a - 3) (2 a + 3)}$ =

= $\frac{a + a + 3}{(2 a - 3) (2 a + 3)} =$ $\frac{(2 a + 3)}{(2 a - 3) (2 a + 3)} =$ $\frac{1}{2 a - 3}$ .