Question

Ajutor ...e urgent ...
Exercitiile incercuite cu rosu

Answer 1

Răspuns si Explicație pas cu pas: In atasament

Answer 2

Ex. 2

a)
$\it \frac{2}{x \: - \: 2} \: + \: \frac{x \: + \: 2}{x \: + \: 1} \cdot ( \frac{x \: - \: 1}{x \: + \: 2} \: - \frac{6}{x \: - \: 2} ) = \frac{2}{x \: - \: 2} \: + \: \frac{x \: + \: 2}{x \: + \: 1} \cdot \frac{(x \: - \: 2)(x \: - \: 1) \: - \: 6(x \: + \: 2)}{(x \: + \: 2)(x \: - \: 2)} = \frac{2}{x \: - \: 2} \: + \: \frac{x \: + \: 2}{x \: + \: 1} \cdot \frac{x ^{2} - x - 2x + 2 - 6x - 12}{(x \: + \: 2)(x \: - \: 2)} = \frac{2}{x - 2} + \frac{1}{x \: + \: 1} \cdot \frac{x ^{2} - x - 2x + 2 - 6x - 12 }{x - 2} = \frac{2}{x \: - \: 2} + \frac{1}{x \: + \: 1} \cdot \frac{ {x}^{2} - 9x - 10 }{x \: - \: 2} = \frac{2}{x \: - \: 2} + \frac{1}{x \: + \: 1} \cdot \frac{ {x}^{2} + x - 10x - 10}{x \: - \: 2} = \frac{2}{x \: - \: 2} + \frac{1}{x \: + \: 1} \cdot \frac{x(x \: + \: 1) - 10(x \: + \: 1)}{x \: - \: 2} = \frac{2}{x \: - \: 2} + \frac{1}{x \: + \: 1} \cdot \frac{(x \: + \: 1)(x \: - \: 10)}{x \: - \: 2} = \frac{2}{x - 2} + \frac{x \: - \: 10}{x - 2} = \frac{2 \: + \: x - \: 10}{x \: - \: 2} = \frac{ - 8 \: + \: x}{x \: - \: 2}$
b)
$\it \frac{x \: + \: 2}{x \: + \: 1} \cdot ( \frac{x \: + \: 1}{ x \: + \: 2} - \frac{ {x}^{2} - 1}{ {x}^{2} - 4} ) \: + \: \frac{x \: - \: 1}{x \: - \: 2} = \frac{x \: + \: 2}{x \: + \: 1} \cdot ( \frac{x \: + \: 1}{ x \: + \: 2} - \frac{ {x}^{2} - 1 }{(x - 2)(x + 2)} ) \: + \: \frac{x \: - \: 1}{x \: + \: 2} = \frac{ x \: + \: 2}{x \: + \: 1} \cdot \frac{(x \: + \: 1)(x \: - \: 2) - (x ^{2} - 1) }{(x \: - \: 2)(x \: + \: 2)} \: + \: \frac{x \: - \: 1}{x \: - \: 2} = \frac{1}{x \: + \: 1} \cdot \frac{ {x}^{2} + x - 2x - 2 - {x}^{2} + 1}{x \: - \: 2} + \frac{x \: - \: 1}{x \: - \: 2} = \frac{1}{x \: + \: 1} \cdot ( \frac{ - x - 1}{x \: - \: 2} ) + \frac{x \: - \: 1}{x \: - \: 2} = \frac{1}{x \: + \: 1} \cdot ( \frac{ - (x \: + \: 1)}{x \: - \: 2)} ) \: + \: \frac{x \: - \: 1}{x \: - 2} = \frac{ - 1}{x \: - \: 2} \: + \: \frac{x \: - \: 1}{x \: - \: 2} = \frac{ - 1 \: + \: x \: - \: 1}{x \: - \: 2} = \frac{x \: - \: 2}{x \: - \: 2} = 1$