190 Вправа 190Алгебра 8 клас Бевз 2025 · § 4 · стор. 40

Умова

Виконай дії.

190. Виконай дії.

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

= $\frac{2^{∖ x - 2 a}}{x + 2 a} + \frac{3^{∖ x + 2 a}}{x - 2 a} + \frac{2 a - 3 x}{(x - 2 a) (x + 2 a)}$ =

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

= $\frac{2 x - 4 a + 6 a + 3 x + 2 a - 3 x}{(x - 2 a) (x + 2 a)} =$ $\frac{2 x + 4 a}{(x - 2 a) (x + 2 a)}$ =

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

б) $\frac{2}{x + 4} - \frac{x - 3}{x^{2} - 4 x + 16} - \frac{x^{2} - 9 x}{x^{3} + 64}$ =

= $\frac{2^{∖ x^{2} - 4 x + 16}}{x + 4} - \frac{{x - 3}^{∖ x + 4}}{x^{2} - 4 x + 16} - \frac{x^{2} - 9 x}{(x + 4) (x^{2} - 4 x + 16)}$ =

= $\frac{2 (x^{2} - 4 x + 16) - (x - 3) (x + 4) - (x^{2} - 9 x)}{(x + 4) (x^{2} - 4 x + 16)}$ =

= $\frac{2 x^{2} - 8 x + 32 - x^{2} - x + 12 - x^{2} + 9 x}{(x + 4) (x^{2} - 4 x + 16)}$ =

= $\frac{44}{(x + 4) (x^{2} - 4 x + 16)} =$ $\frac{44}{x^{3} + 64}$ ;

в) $\frac{1}{a - 2} - \frac{3}{a + 2} + \frac{3 a - 10}{a^{2} - 4}$ =

= $\frac{1^{∖ a + 2}}{a - 2} - \frac{3^{∖ a - 2}}{a + 2} + \frac{3 a - 10}{(a - 2) (a + 2)}$ =

= $\frac{a + 2 - 3 (a - 2) + 3 a - 10}{(a - 2) (a + 2)} =$ $\frac{a + 2 - 3 a + 6 + 3 a - 10}{(a - 2) (a + 2)}$ =

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

г) $\frac{3}{(x - a) (x - c)} + \frac{2}{(x - a) (c - a)} - \frac{2}{(c - x) (a - c)}$ =

= $\frac{3^{∖ a - c}}{(x - a) (x - c)} - \frac{2^{∖ x - c}}{(a - c) (x - a)} + \frac{2^{∖ x - a}}{(a - c) (x - c)}$ =

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

= $\frac{(a - c)}{(x - a) (x - c) (a - c)} =$ $\frac{1}{(x - a) (x - c)}$ .