Question

Dau coroana!..............................

Answer 1

(x+1)/(x-5) + (x-1)/(x+5) = (7x+5)/(x^2-25)
Observam ca x^2-25 = (x+5)(x-5).
Pentru a aduce toata ecuatia la acelasi numitor amplificam prima fractie cu (x+5) si a doua fractie cu (x-5)

(x+1)(x+5)/(x^2-25) + (x-1)(x-5)/(x^2-25) = (7x+5)/(x^2-25)
(x+1)(x+5) + (x-1)(x-5) = 7x+5
x^2 + 5x + x + 5 + x^2 - 5x - x + 5 = 7x + 5
2x^2 + 10 - 7x -5 = 0
2x^2 - 7x + 5 = 0
Delta = b^2-4ac = 49-40 = 9
x1,2 =(-b+sau-radical din delta)/2a
x1,2 = (7+sau-3)/4
x1 = 10/4 = 5/2
x2 = 4/4 = 1
 

Answer 2

numitorul comun e x^2-25  ( x-5)(x+5)

prima fractie se amplifica cu x+5 , a doua cu x-5

[(x+1)(x+5) + (x-1) ( x-5)]/ (x^2-25)= (7x+5)/(x^2-25)
egalez numaratorii 

x^2+5x+x+5+x^2-5x-x+5=7x+5
2x^2+10=7x+5
2x^2-7x+5=0
Δ= 7^2-4*2*5=49-40=9
x1 = (7+V9)/4=(7+3)/4=10/4=5/2
x2=  (7-3)/4=4/4=1
Solutiile sunt : 5/2 si 1