Question

спростіть вираз: у+3/2у+2 - у+1/2у-2+3/у2-1

Answer 1

$\frac{y+3}{2y+2} - \frac{y+1}{2y-2}+ \frac{3}{y^{2}-1}= \frac{y+3}{2(y+1)}- \frac{y+1}{2(y-1)} + \frac{3}{(y-1)(y+1)} = \\ \\ = \frac{(y+3)(y-1)-(y+1)(y+1)+6}{2(y+1)(y-1)}= \frac{ y^{2}+2y-3-y^{2}-2y-1+6 }{2(y+1)(y-1)} = \frac{2}{2(y+1)(y-1)} = \\ \\ = \frac{1}{y^{2}-1}$