Question

докажите тождество 228

Answer 1

$displaystyle left(frac{8y^2+2y}{8y^3-1}-frac{2y+1}{4y^2+2y+1}right)cdotleft(1+ frac{2y+1}{2y}-frac{4y^2+10y}{4y^2+2y}right):frac{1}{2y}= \ \ left(frac{8y^2+2y}{(2y-1)(4y^2+2y+1)}-frac{2y+1}{4y^2+2y+1}right)cdot \ \ left(1+ frac{2y+1}{2y}-frac{4y^2+10y}{2y(2y+1)}right):frac{1}{2y}= \ \ frac{8y^2+2y-(2y+1)(2y-1)}{(2y-1)(4y^2+2y+1)}cdot \ \ frac{2y(2y+1)+(2y+1)^2-4y^2-10y}{2y(2y+1)}: frac{1}{2y}=$
$displaystyle frac{8y^2+2y-4y^2+1}{(2y-1)(4y^2+2y+1)}cdot frac{4y^2+2y+4y^2+4y+1-4y^2-10y}{2y(2y+1)}:frac{1}{2y}= \ \ frac{4y^2+2y+1}{(2y-1)(4y^2+2y+1)}cdot frac{4y^2-4y+1}{2y(2y+1)}: frac{1}{2y}= \ \ frac{1}{2y-1}cdot frac{(2y-1)^2}{2y(2y+1)}cdot2y= frac{2y-1}{2y+1}$