Question

va rog mult,am nevoie de ajutorul vostru urgent!!!

Answer 1

[tex] \frac{x^{2}-2}{x^{2}+x} - \frac{1}{x+1}= \frac{2x-3}{x} \rightarrow \frac{x^{2}-2}{x(x+1)}- \frac{x}{x(x+1)}= \frac{2x-3}{x} \rightarrow \frac{x^{2}-x-2}{x(x+1)}= \frac{2x-3}{x} \rightarrow \\ \frac{x^{2}-2x+x-2}{x+1}= 2x-3 \rightarrow x(x-2)-1(x-2)= (x+1)(2x-3) \rightarrow \\ \\ x^{2}-x-2=2x^{2}-3x+2x-3 \rightarrow 2x^{2}-x^{2}-x+x-3+2=0 \rightarrow \\ \\ (x^{2}-1)=0 \rightarrow x= -1, x=1 \\ \\ S= 1\\   [/tex]
daca x= -1 atunci numitorul devine 0, iar fractia nu are sens. deci singura solutie e +1. 

Answer 2

x² - 2/x² + x - 1/x + 1 = 2x - 3/x
(x² - 2)/x(x + 1) - x/x(x + 1) = (2x - 3)(x + 1)/x(x + 1)
(x² - x - 2)/x(x + 1) = 2x² + 2x - 3x - 3)/x(x + 1)
(x² - x - 2 - 2x² + x + 3)/x(x + 1) = 0
(- x² + 1)/x(x + 1) = 0
- (x² - 1)/x(x + 1) = 0
- (x + 1)(x - 1)/x(x + 1) = 0           | : (x + 1)
- (x - 1)/x = 0
x = 0
- x = 1
x = - 1