Question

Efectueaza operatiile si scrie rezultatul ca o fractie ireductibila:
a.)y+2 pe 2y+1 - 2y-3 pe 2y+1
b.)x+1 pe 3x + 2-x pe 4x

Answer 1

$a) \frac{y + 2}{2y + 1} - \frac{2y - 3}{2y + 1} = \frac{y + 2 - (2y - 3)}{2y + 1} = \frac{y + 2 - 2y + 3}{2y + 1} = \frac{(y - 2y) + (2 + 3)}{2y + 1} = \frac{ - y + 5}{2y + 1} = \frac{5 - y}{2y + 1} \\ \\ b) \frac{x + 1}{3x} + \frac{2 - x}{4x} = \frac{(x + 1) \times 4 + (2 - x) \times 3}{3x \times 4} = \frac{4(x + 1) + (2 - x) \times 3}{3x \times 4} = \frac{4(x + 1) + 3(2 - x)}{3x \times 4} = \frac{4x + 4 + 6 - 3x}{3x \times 4} = \frac{(4x - 3x) + (4 + 6)}{3x \times 4} = \frac{x + 10}{12x}$