Question

Сократите дроби:

1) 5-20a^2/20a+10

2) 3x^2+8x-3/x^2+3x

3) y^3+7y^2-60y/10y-50

Answer 1

1) $frac{5-20a^2}{20a+10} = frac{(-1)*(-5)+(-5)*4a^2}{10*2a+10*1} = frac{(-5)*[(-1)+4a^2]}{10(2a+1)} = -frac{5*[(2a)^2-(1)^2]}{5*2*(2a+1)} =$
$=-frac{[2a-1]*[2a+1]}{2*(2a+1)} = -frac{2a-1}{2} = frac{1-2a}{2}= frac{1}{2}- frac{2a}{2}= frac{1}{2}-a$
2) $frac{3x^2+8x-3}{x^2+3x} = frac{3x^2+9x-x-3}{x(x+3)}= frac{3x(x+3)-(x+3)}{x(x+3)}= frac{(3x-1)(x+3)}{x(x+3)}= frac{3x-1}{x}$
3) $frac{y^3+7y^2-60y}{10y-50} = frac{y(y^2+7y-60)}{10(y-5)} = frac{y(y^2-5y+12y-12*5)}{10(y-5)}=$
$=frac{y[(y-5)(y+12)]}{10(y-5)} = frac{y(y-5)(y+12)}{10(y-5)} = frac{y(y+12)}{10}$