Question

Buna! Ma puteti ajuta va rog? Am nevoie de ajutor... ​

Answer 1

Explicație pas cu pas:

a)

x≠2; x≠1; x≠-2

$= \dfrac{4(x + 2)}{x - 2} \cdot \bigg( \dfrac{x + 4}{2(x - 1)} - \dfrac{5x + 2}{(x - 1)(x + 2)} \bigg)$

$= \dfrac{4(x + 2)}{x - 2} \cdot \dfrac{(x + 4)(x + 2) - 2(5x + 2)}{2(x - 1)(x + 2)}$

$= \dfrac{2}{x - 2} \cdot \dfrac{ {x}^{2} + 6x + 8 - 10x - 4}{x - 1}$

$= \dfrac{ 2({x}^{2} - 4x + 4)}{(x - 2)(x - 1)} = \dfrac{ 2{(x - 2)}^{2}}{(x - 2)(x - 1)}$

$= \bf \dfrac{ 2(x - 2)}{x - 1}$

b)

x≠-1; x≠4; x≠±2

$= \dfrac{x - 2}{3(x + 1)} : \bigg(\dfrac{x + 5}{3(x - 4) } - \dfrac{2x + 3}{(x + 1)(x - 4)}\bigg)$

$= \dfrac{x - 2}{3(x + 1)} : \dfrac{(x + 5)(x + 1) - 3(2x + 3)}{3(x - 4)(x + 1) }$

$= \dfrac{x - 2}{3(x + 1)} : \dfrac{ {x}^{2} + 6x + 5 - 6x - 9}{3(x - 4)(x + 1) }$

$= \dfrac{x - 2}{3(x + 1)} : \dfrac{ {x}^{2} - 4}{3(x - 4)(x + 1) } = \dfrac{x - 2}{3(x + 1)} : \dfrac{(x - 2)(x + 2)}{3(x - 4)(x + 1) }$

$= \dfrac{x - 2}{3(x + 1)} \cdot \dfrac{3(x - 4)(x + 1)}{(x - 2)(x + 2)}$

$= \bf \dfrac{x - 4}{x + 2}$