Vũ Xuân Đăng
Giới thiệu về bản thân
$$\frac{BC}{CD} = \frac{AB}{DE} \Rightarrow \frac{x}{7,2} = \frac{5}{15}$$
$$\Rightarrow x = \frac{7,2 \cdot 1}{3} = 2,4$$Vậy $x = 2,4$.
a. $$\left( \frac{2x}{3x+1} - 1 \right) = \frac{2x - (3x+1)}{3x+1} = \frac{2x - 3x - 1}{3x+1} = \frac{-x-1}{3x+1}$$
$$\left( 1 - \frac{8x^2}{9x^2-1} \right) = \frac{(9x^2-1) - 8x^2}{9x^2-1} = \frac{x^2-1}{9x^2-1}$$ $$\frac{x^2-1}{9x^2-1} = \frac{(x-1)(x+1)}{(3x-1)(3x+1)}$$ $$P = \frac{-x-1}{3x+1} : \frac{(x-1)(x+1)}{(3x-1)(3x+1)}$$ $$P = \frac{-(x+1)}{3x+1} \cdot \frac{(3x-1)(3x+1)}{(x-1)(x+1)}$$b.
$$P = \frac{1 - 3 \cdot 2}{2 - 1}$$ $$P = \frac{1 - 6}{1}$$ $$P = -5$$$$\left(\frac{2x-50}{50} - 1\right) + \left(\frac{2x-51}{49} - 1\right) + \left(\frac{2x-52}{48} - 1\right) + \left(\frac{2x-53}{47} - 1\right) + \left(\frac{2x-200}{25} + 4\right) = 0$$
$$\frac{2x-100}{50} + \frac{2x-100}{49} + \frac{2x-100}{48} + \frac{2x-100}{47} + \frac{2x-100}{25} = 0$$
$$(2x - 100) \cdot \left( \frac{1}{50} + \frac{1}{49} + \frac{1}{48} + \frac{1}{47} + \frac{1}{25} \right) = 0$$ $$2x - 100 = 0$$ $$2x = 100$$ $$x = 50$$$$\left(\frac{2x-50}{50} - 1\right) + \left(\frac{2x-51}{49} - 1\right) + \left(\frac{2x-52}{48} - 1\right) + \left(\frac{2x-53}{47} - 1\right) + \left(\frac{2x-200}{25} + 4\right) = 0$$
$$\frac{2x-100}{50} + \frac{2x-100}{49} + \frac{2x-100}{48} + \frac{2x-100}{47} + \frac{2x-100}{25} = 0$$
$$(2x - 100) \cdot \left( \frac{1}{50} + \frac{1}{49} + \frac{1}{48} + \frac{1}{47} + \frac{1}{25} \right) = 0$$ $$2x - 100 = 0$$ $$2x = 100$$ $$x = 50$$- $$\frac{2xy - x - 2xy - y}{xy} = \frac{-x - y}{xy}$$
$\frac{-(x + y)}{xy}$