Question

1. Se considera triunghiul ABC si punctele D apartine (AB), E apartine AC , asfel incat DE || BC
  Daca AD/ AB=3/8 si AC=24 cm , lungimea segmentului EC = ... 
2. aduceti la o forma mai simpla expresia : E(x)=2x+1/x-1 : (1- 3x la a doua / 1-x la a doua) 
 x apartine R\ {-1/2 ; -1; 1; 1/2} 
 3. Aratati ca nr. n=5x 10 la 100 +22 se divide cu 9

Answer 1

ΔADE≈ΔABC⇒prin teorema lui Thales
AD/AB=AE/AC
3/8=AE/24
AE=3*24/8=3*3=9
EC=AC-AE
=24-9=15

2x+1/x-1 *1-x²/1-3x²
2x+1/x-1 * -(x²-1)/3x²-1
2x+1/x-1 *-(x-1)(x+1)/3x²-1  se simplifica si ne da
-(2x+1)(x+1)/3x²-1
-(2x²+2x+x+1)/3x²-1
-2x²-3x-1/3x²-1
-2x²-2x-x-1/3x²-1
-2x(x+1)-(x+1)/3x²-1
-(2x+1)(x+1)/3x²-1
-(2x+1)(x+1)/x²-1+2x²
-(2x+1)(x+1)/(x-1)(x+1)+2x²
-(2x+1)/(x-1)+2x²