Question

Упростите плиз 4/y - 2/y-5 + 2y+10/25-y^2

Answer 1

$frac{4}{y} - frac{2}{y-5} + frac{2y+10}{25-y^{2}} =$$frac{4}{y} - frac{2}{y-5} + frac{2y+10}{(5+y)(5-y)} =$$frac{4}{y} + frac{2}{5-y} + frac{2y+10}{(5+y)(5-y)} =$$frac{4(5+y)(5-y) +2y(5+y) + y(2y + 10)}{y(5+y)(5-y)} =$$frac{100-4y^{2} + 10y + 2y^{2} + 2y^{2} + 10y}{y(5+y)(5-y)} =$$frac{100+20y}{y(5+y)(5-y)} = frac{20(5+y)}{y(5+y)(5-y)} =$$frac{20}{y(5-y)}$

Ответ: $frac{20}{y(5-y)}$