Question

упростите. заранее спасибо
а)х+5/5х-25 - 3х+5/х²-25
б)у-8/4у-16 + 4/у²-4у

Answer 1

$frac{x+5}{5x-25} -frac{3x+5}{x^2-25} =frac{x+5}{5(x-5)} -frac{3x+5}{(x-5)(x+5)} = frac{(x+5)(x+5)}{5(x-5)(x+5)} -frac{5(3x+5)}{5(x-5)(x+5)} =\ =frac{(x+5)^2-5(3x+5)}{5(x^2-25)} =frac{x^2+10x+25-15x-25}{5(x^2-25)} =frac{x^2-5x}{5(x^2-25)}=\=frac{x(x-5)}{5(x-5)(x+5)} = frac{x}{5(x+5)}$

$frac{y-8}{4y-16} +frac{4}{y^2-4y} =frac{y-8}{4(y-4)} +frac{4}{y(y-4)}= frac{y(y-8)}{4y(y-4)} +frac{4*4}{4y(y-4)}= \ = frac{y(y-8)+4*4}{4y(y-4)} =frac{y^2-8y+16}{4y(y-4)}= frac{(y-4)^2}{4y(y-4)} =frac{y-4}{4y}$