Контрольные задания > 8 кл. Алгебра ср. упростите 1) $\frac{y}{4} + \frac{y-2}{5}$ 2) $\frac{2x-1}{3} - \frac{x+2}{6}$ 3) $\frac{c+3}{c^2} - \frac{1}{c}$ 4) $\frac{2x}{a} \cdot \frac{a}{8x}$ 5) $\frac{y^2+3y}{4} \cdot \frac{y}{2y+6}$ 6) $\frac{y^2-9}{27y^2} \cdot \frac{9y}{y-3}$ 7) $\frac{3a^2}{b} : \frac{b}{a^3}$ 8) $-\frac{2x^2}{y} : \frac{6x^3}{y^2}$ 9) $\frac{xy+y^2}{a-3b} : \frac{x^2-y^2}{2a-6b}$ 10) $\frac{a+b}{3a-b} + \frac{1}{a+b} \cdot \frac{a^2-b^2}{3a-b}$
Вопрос:

8 кл. Алгебра ср. упростите 1) $$\frac{y}{4} + \frac{y-2}{5}$$ 2) $$\frac{2x-1}{3} - \frac{x+2}{6}$$ 3) $$\frac{c+3}{c^2} - \frac{1}{c}$$ 4) $$\frac{2x}{a} \cdot \frac{a}{8x}$$ 5) $$\frac{y^2+3y}{4} \cdot \frac{y}{2y+6}$$ 6) $$\frac{y^2-9}{27y^2} \cdot \frac{9y}{y-3}$$ 7) $$\frac{3a^2}{b} : \frac{b}{a^3}$$ 8) $$-\frac{2x^2}{y} : \frac{6x^3}{y^2}$$ 9) $$\frac{xy+y^2}{a-3b} : \frac{x^2-y^2}{2a-6b}$$ 10) $$\frac{a+b}{3a-b} + \frac{1}{a+b} \cdot \frac{a^2-b^2}{3a-b}$$

Ответ:

  1. $$\frac{y}{4} + \frac{y-2}{5} = \frac{5y + 4(y-2)}{20} = \frac{5y + 4y - 8}{20} = \frac{9y-8}{20}$$
  2. $$\frac{2x-1}{3} - \frac{x+2}{6} = \frac{2(2x-1) - (x+2)}{6} = \frac{4x - 2 - x - 2}{6} = \frac{3x - 4}{6}$$
  3. $$\frac{c+3}{c^2} - \frac{1}{c} = \frac{c+3 - c}{c^2} = \frac{3}{c^2}$$
  4. $$\frac{2x}{a} \cdot \frac{a}{8x} = \frac{2x \cdot a}{a \cdot 8x} = \frac{2ax}{8ax} = \frac{1}{4}$$
  5. $$\frac{y^2+3y}{4} \cdot \frac{y}{2y+6} = \frac{y(y+3)}{4} \cdot \frac{y}{2(y+3)} = \frac{y^2(y+3)}{8(y+3)} = \frac{y^2}{8}$$
  6. $$\frac{y^2-9}{27y^2} \cdot \frac{9y}{y-3} = \frac{(y-3)(y+3)}{27y^2} \cdot \frac{9y}{y-3} = \frac{(y-3)(y+3) \cdot 9y}{27y^2 \cdot (y-3)} = \frac{9y(y+3)(y-3)}{27y^2(y-3)} = \frac{y+3}{3y}$$
  7. $$\frac{3a^2}{b} : \frac{b}{a^3} = \frac{3a^2}{b} \cdot \frac{a^3}{b} = \frac{3a^2 \cdot a^3}{b \cdot b} = \frac{3a^5}{b^2}$$
  8. $$-\frac{2x^2}{y} : \frac{6x^3}{y^2} = -\frac{2x^2}{y} \cdot \frac{y^2}{6x^3} = -\frac{2x^2 \cdot y^2}{y \cdot 6x^3} = -\frac{2x^2y^2}{6x^3y} = -\frac{y}{3x}$$
  9. $$\frac{xy+y^2}{a-3b} : \frac{x^2-y^2}{2a-6b} = \frac{y(x+y)}{a-3b} \cdot \frac{2(a-3b)}{(x-y)(x+y)} = \frac{y(x+y) \cdot 2(a-3b)}{(a-3b)(x-y)(x+y)} = \frac{2y}{x-y}$$
  10. $$\frac{a+b}{3a-b} + \frac{1}{a+b} \cdot \frac{a^2-b^2}{3a-b} = \frac{a+b}{3a-b} + \frac{(a-b)(a+b)}{(a+b)(3a-b)} = \frac{a+b}{3a-b} + \frac{a-b}{3a-b} = \frac{a+b+a-b}{3a-b} = \frac{2a}{3a-b}$$
Смотреть решения всех заданий с листа

Похожие